Ha! Missed that important caveat! Thanks!
Interesting though that a person could see themselves as a CS, but not an engineer. The overlap is quite striking. At the end of the day, CS and engineering, at their most interesting and non-rote level, both involve synthesis of new information from previously known information and experiences. In a nutshell they are both problem solving. Maybe they have a misconception of engineering? 
UCLA would be considered a reach for any student applying for the CS major.
CSULA would be much easier to get into, CS or otherwise.
Exactly. Most people think of the remaining HYPSM schools as being strong STEM schools but always leave out Yale.
Yale wants to change this reputation, which is why unlike the others, it favors strong STEM kids in admissions. To illustrate how much they care, it is the only one that sends out likely letters explicitly for the strongest STEM applicants in RD, and (during non-COVID times) invites these likely letter recipients to a special weekend created just for them called Yale Engineering and Science Weekend (YES-W), followed by Bulldog Days which is meant for everyone admitted to Yale.
But the same advice applies to kids that are not quite strong enough to get those likely letters. Excellent, but not quite national level STEM students are still more likely to get into Yale than into its peers. We saw this personally with a couple of my son’s friends.
If you are a California resident, consider UC Merced. Very likely admit for students with high end stats, not huge, and declaring the CSE major is not difficult: Declaration of Major | Engineering Academic Advising
Other typical science and math majors are available: applied mathematical sciences, biological sciences, chemical sciences, environmental systems sciences, and physics are available: UC Merced Majors and Minors Programs | Apply Today . However, pure math and statistics may be limited in offerings.
But note that many STEM majors have prerequisite sequences that must be completed in frosh/soph years if the student wants to be able to complete the degree in eight semesters. I.e. choosing such a major in fourth semester having taken none of the prerequisites likely means graduating late.
In other words, just because all of the possible majors are open admission to declare them does not mean that the student can ignore planning courses for the majors starting in the first semester.
For CS, that is a concern. For example, Swarthmore rations CS courses for CS majors (and presumably non-CS majors are even lower on the list to register for them), and one Williams parent has posted on the forums that some prospective CS major frosh have been unable to register for the first CS course during both semesters of frosh year.
Math is likely to be less of a concern, since demand for math seems to be more stable. Physics is generally not a concern, since it is not too popular a major – a more likely concern at some small schools is that the major is so unpopular that the physics department is too small to consistently offer all of the usual upper level physics courses.
Besides CS, the most popular type of STEM major is usually biology (other than at engineering-heavy schools like MIT and the “mines” schools).
Aren’t they too small to accommodate a STEM student? In the sense of having too few classes to keep a STEM kid occupied as their interests develop?
I can see Wesleyan ( but Amherst and Williams?)
Continuing thanks for the input!
To clarify the engineering/cs issues about this kid (though I want to keep the comments coming for the benefit of all):
Someone told me once that there are two kinds of science people: the “how?” people and the “why?” people. Engineers are the “how” people. Kiddo is a “why” person. He is in it for figuring out why things happen, in a pure science/math kind of way. Wouldn’t be surprised if he ends up as an academic.
He has dabbled in programming on the side as the need arises, hangs with the cs kids, and has cs in his genetic code (see what I did there? Lol), but is not interested in majoring in it. He sees it as a tool, not a trade. That could change, and if it does, it will be intense. So a really strong cs department would be important- even if he goes in as a math/physics type.
Safeties/Matches in a range of sizes: DePaul, U Dayton, Grinnell, Stevens Institute of Tech, Rose Hulman, Clemson, Trinity (CT), RPI, RIT, College of Charleston, Marist, Miami Ohio, Connecticut College, Knox, Hendrix
Good point. I am guessing this kid would go all in with stem pre-reqs just for fun. He is knocking it out of the park taking calc BC and advanced physics as a junior - so he could in theory place out of some reqs. But point well taken - he needs to make sure he takes the right courses to keep his options open, and that the school structures those reqs appropriately/accessibly.
Another thought I had is maybe Oxbridge - but I can’t decide if he is focused in the right way. He is definitely stem, and is advanced enough, but is he focused enough?
He should be a physics major.
I’m going to second The University of Rochester (in Rochester, NY). It seems to fly under the radar for many, but is a hidden gem for STEM and “not sure exactly what.”
For anyone coming from further away, it’s also 15 minutes from the airport. A lot of good schools are tougher to get to.
If you don’t have a cost constraint, safeties are easy. There are a bunch of state flagships that are safeties for someone even considering the very top schools.
Generally speaking, I’d say, there’s enough depth for someone like the OP’s S22 who arrives not knowing what they want to specialize in. They will specialize in whatever it is their professors are passionate about. And, that will get them into graduate school, medical school - wherever they want to go. The problem may crop up with science prodigies who have already burned through what was offered in high school and are well on their way to doing poster presentations of their own work. The really pointy kids may have a problem finding a LAC that suits them.
Anyway, that’s my $.02.
The issue with this approach is - I could be wrong - the need to declare a major, or at least to apply to a department/school within the flagship, at the time of admissions. Seems like a lot of such schools put CS in the engineering school. If kiddo applies as a math major or physics major, doesn’t that foreclose the cs major option? And many of the flagships are over enrolled in cs, and therefore not as safe of a safety for an oos student. It is a catch 22.
So the oos flagship means a lot of digging in a lot of state schools to find out if they are structured for an undeclared stem kid. And honestly, as a California resident, I am not inclined to pay oos tuition when we have the UCs. Which brings me back full circle to where the UCs all are in the safety-match-reach continuum for a non-maybe cs stem kid.
There are MANY fields that search for “why?” including…engineering. Of the practicing engineers, having the “why?” gene can be beneficial. My son is very much cut from that cloth. @boneh3ad is a research engineer and could expand on how one might, as he did, pursue the “why?” path in engineering. I wouldn’t write the whole field off based on an off the cuff conversation. The possibilities are vast. I’m beating this dead horse because as @ucbalumnus mentioned, course sequencing is very important.
I would certainly look at Harvey Mudd based on the little I’ve read here about your son.
I know absolutely zero about University of Rochester.
Sounds cold. 
Putting it on the list to research- along with many others mentioned upthread. You don’t know how happy this makes me! I will be busy putting together my spreadsheet for a few weeks! 
If he wants to us programming as a tool, the need for formal education isn’t really necessary.
I know a guy who did a biology PhD and had to do some programming as part of his thesis. He was self taught. His main advisor made him clean up us code and fully document it so that others could follow easily. In learning to code with proper best practices, he became good enough that he does that now does exclusively for Facebook doing bioinformatics and nothing to do with his biology PhD per se at all .
My son codes in multiple languages. He either learned them as part of a course that required it or he self taught. The only formal CS course he took was a grad class in Deep Learning (different types of neural networks, etc.)
Totally agree with this. Kiddo is 17, imo too young to decide anything about what he wants to do. I am all about keeping his options as open as possible for as long as possible. That’s what worries me about having to pick your path before you even get to campus.
So many young hopefuls posting on CC seem to want to commit to engineering or cs, and I scratch my head wondering how they know that.
Here’s the thing…they have to commit to SOMETHING at sometime. From there, as their knowledge base grows, they evolve in their interests.
My son chose the antithesis of what you’re looking for…ME at Cal Poly (from OOS with no interest in any other CA public schools). That’s what you are on day one, a Mechanical Engineering student on a very specific ME path. As he learned more about engineering he was certain that he wanted to design hardware. The more he learned about that, he didn’t want to be confined to reiterating a small piece of a big thing over and over. He became interested in testing because that let him design unique and different complete hardware that he got to oversee. He’d previously said he’d never want to do testing. Now, as he’s gotten even deeper into the theoretical side of what he does, he’s expressed an interest in academics, something he once said he had zero interest in. Had he not taken this path however, he’d still be wandering, trying to figure out what he wanted to do.
The point is, they change, and they can only change on top of a foundation.
You both should read So Good They Can’t Ignore You by Cal Newport. It speaks directly to the conundrum you’re trying to solve.