Exactly.
Leave some money in the bank for medical school. Your daughter does not want to graduate with an MD degree and $400,000 in debt from medical school. There are a LOT of universities that are very good for premed students, including your in-state public schools and some WUE/WICHE schools.
Here I have mixed reaction. Perhaps most important, the large majority of students who start off thinking “premed” end up doing something else. Biomedical engineering is a very good example of “something else”. It seems unlikely to me that any form of engineering is the easiest way to maintain a medical-school-worthy GPA. However, I have to admit that one daughter was taking extra math and physics classes to offset a B- in organic chemistry. What one student thinks of as a brutally difficult class might be what another student thinks of as a likely A or even A+.
And whether to focus on engineering or premed is something that a student can decide when they are part way through university.
And it is not clear to me why you have so many expensive out of state schools on your list. Neither premed nor engineering is an area where “prestige” matters. What you do as an undergraduate student is going to matter a lot more than where you do it. Both engineering and premed classes will include quite a few classes which are very academically demanding, and that are full of very strong students at any of a very wide range of universities.
I have asked two doctors who I know where the other students in their MD program had gotten their bachelor’s degree. An exact quote from one of them is: “all over the place”. We found the same thing listening into a daughter’s opening ceremony for her DVM program. It was rare to hear the same school mentioned twice. We see the same thing in both my wife’s medical-related master’s program and our other daughter’s PhD program in a biomedical field. The students in highly ranked graduate programs, including MD and biomedical engineering programs, come from a wide range of undergraduate universities. You don’t have to spend the big bucks for a bachelor’s degree.
Which also brings up the thought that there are a variety of biomedical fields which are possibilities, but where some graduate schools is likely. PhD programs are usually funded. Master’s degrees are usually not funded (unless obtained by a PhD student who drops out part way through). I might add that admissions to top PhD programs appears to be very, very competitive.
I think that this is something that each student needs to figure out over time. It is very common to figure this out while in university.
As one example, our younger daughter briefly thought of medical school. Due to a change in major she needed to take four lab courses at the same time. She discovered that she loved lab work, and was good at it. She ended up as a biology major. Normally a bachelor’s degree in biology leads to limited job opportunities. However, she had spent so much time in the lab and had so much lab experience that she got a good job pretty quickly after graduating. Her first job to me sounded like almost exactly the same thing that she had already been doing in university.
In terms of biomedical engineering, it might depend upon how your daughter takes to it. Some students do get A’s in those courses.
I think that OSU should be on your list. I would also look at the WUE school finder and see what it recommends. I am pretty sure that UC Merced is a WUE school, but I am also pretty sure that there are restrictions on what major a student chooses to get a WUE discount, and I do not know which majors this would apply to.