You might want to read the “applying sideways” blog on the MIT admissions web site. As I understand it, it recommends that students do what is right for them, do it well, and treat people well. This means that when thinking about options for high school, you ignore university admissions, and instead do what is right for the student. Things will work out.
This is what our family has done and it has worked out well for us in terms of university admissions and otherwise. This did include admissions to some highly ranked schools. In terms of “do what is right for the student” we each did very different things (including attending very different high schools). We just each did what was right for us individually.
The other thing that occurs to me reading your post is that high school students in the US are on average and in general under way, way too much stress. Just being a teenager and finding your way in life is stressful enough. Adding in thoughts of whatever you need to do to get into university is just too much, particularly since university admissions in the US is so unpredictable and the top ranked schools are so difficult to get into.
Also, a high school student IMHO should not be spending 3 to 4 hours per night doing homework unless they want to do it. The desire to do this needs to come from inside the student. I did attend universities that require a lot of work and have some experience dealing with this much stress. If you want to do it then it can be fun, but if you don’t want to do it then it can be very unpleasant and mostly likely will not lead to good results. I would be very cautious about this.
There are however a huge number of very good liberal arts colleges and very good universities in the US. If a student does what is right for them, does it well, and gets good grades, and applies to an appropriate range of schools, and if they are a good student, they will get accepted to some colleges and/or universities that are a good fit for them.
By the way both one daughter and I attended high schools that did not offer an AP classes at all. We both nonetheless did fine wrt university admissions.