My husband who has a PhD in aerospace engineering is saying the same thing- that he should do Physics. I sometimes think he might be interested in a quantitative research/ applied Econ/math type program (that is my line of work). We think an engineering background is good for him- but ultimately don’t see him as an engineer as his career path.
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For the Arizona publics:
University of Arizona:
Scholarships: Types of Aid: Incoming First-Year and Transfer Tuition Scholarship Awards | Office of Scholarships & Financial Aid
CS change major or declaration requirements: https://www.cs.arizona.edu/undergraduate/pre-major
Arizona State University:
Scholarships: https://scholarships.asu.edu/estimator
CS change major or declaration requirements (appears to be the same as transfer admission requirements): https://webapp4.asu.edu/programs/t5/majorinfo/ASU00/ESCSEBS/undergrad/false
Whether or not UC Merced is better than UA or ASU depends on other preferences (e.g. specific course and major offerings that the student could be interested in, location, size, etc.).
Or throw them all in as safety / very likely schools and let him decide later if they are what it comes down to in the end.
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That’s a great way to think about it. My kid likes to go deep so I was wary of small LAC’s ( though I love them for other reasons, like small classes and great undergrad teaching). Definitely lots to think about.
I was the same, fascinated too! That’s when I electively got out of the picture. I didn’t want it to be “my thing.” When the counselor looked at the “narrowed” list I’d compiled she said something to the effect of HOLY COW! This will completely overwhelm him! Don’t get me wrong. I still nerded out over the whole thing. I just didn’t talk with him much about it unless he brought it up. When he did, I was fully prepared to discuss.
Also, I completely lost track of your original intent…safety schools. By definition that means guaranteed admit with their stats AND affordable.
I’d STRONGLY recommend he look at Utah. At worst, he’ll get WUE (150% of instate). At best, it could be tuition free. My son got one free year, a little extra for books, etc. followed by three at in state tuition. They have very strong STEM programs, not just engineering. Their math, chemistry, earth sciense and CS departments are all quite good. The campus is nice. The dorms are great. The student body is crazy about their athletics, even gymnastics. It’s close to some of the prettiest land in the nation. It has great air service. Some might be scared off by the LDS influence. It’s certainly felt, but SLC is only 40% Mormon. My son almost chose it even though it was the easiest admit he applied to. I believe you have to declare as an applicant, but changing majors isn’t hard. The major is really a formality.
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I wouldn’t dismiss them out of hand. Note also that the ones in SD and NM are easy for admissions and relatively affordable. But the student should check the available slates of majors and the offerings in them to see that they have coverage of all of the student’s possible interests.
Note that while the SD and NM mine schools offer geology / earth science majors, the more popular CO mine school does not (it offers geological, geophysical, mining, and petroleum engineering).
I already know better than to share my spreadsheet with anyone. Kiddo probably knows it exists, but he has no idea how deep it goes. And you don’t even want to know what I did with the scatterplots. Every once in a while I can’t control myself and mention my newest revelation (like today - there’s a list of undergrad physics profs who won awards for involving students in their research! How cool is that!).
Somehow he doesn’t appreciate it like you all do. I finally feel seen. 
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My S didn’t know what he wanted to major in when we started the college selection process a few years ago. He wasn’t even sure if it’d be one of the fields in STEM (or economics/finance, or creative writing). When we visited colleges (and we visited a lot of them), we made sure that we visited both the engineering school and the A&S school if that’s how the university is set up. He actually made up his mind on these visits, probably because they made him think harder about his choices. He’s now so commited to his choice that he’s about to start his PhD applications in his area of CS.
Rice is a hard admit but combines the best of a research university and an LAC due to its small size. At Rice students do not have to declare a major until the end of Sophomore year and can major in anything, including any STEM discipline and CS (except architecture and music). Architecture and music require admission through portfolio/audition. It is very easy to change majors, and there is no limit on the number of students in any major. Many students come in thinking they want to major in one thing and may graduate majoring in something else entirely.
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It’s a reach, not a safety, but UNC meets your criteria. Students don’t have to declare until end of Sophomore year and it’s strong in the STEM areas, including CS. Right now it doesn’t have an engineering major other than biomedical engineering (plan to add applied engineering major in 2022, currently only a minor).
Also, I “second” looking at ASU for a safety. My D is strongly considering ASU. We are instate for UNC and she is between UNC and ASU. During the admitted student events, a number of students talked about ease of changing majors and being able to tailor to their interests once they figured out their interests. ASU is decently ranked in CS, engineering and life sciences. I haven’t looked at math and physics, but is strong in the analytics majors. Plus, they are #1 ranked Most Innovative university. With strong stats would also qualify for Barrett Honors which is highly regarded.
I second the recommendation for University of Utah as a safety. You can apply Undecided and later declare a major, even engineering or CS. High academic students can get merit scholarships and it’s easy to gain residency status after your first year.
Other schools that come to mind: Brown because you can self-design your major and Johns Hopkins because, unless you want BME, you don’t need to declare a major when you apply. Hopkins is great for undergrad research and they have the Applied Physics Lab which is very well funded. Dartmouth allows you to switch majors almost up until graduation, provided you have the required courses and the D-plan makes it pretty easy to double major. Notre Dame (check out About // Notre Dame California // University of Notre Dame), Cornell, Rice, UChicago - tons of potential schools depending on his stats and what type of environment he’s looking for.
Good luck!