Why can't we build taller schools, restaurants, and stores at the same time? Or better yet a tower that is a store on the bottom floor, then offices for a couple floors, then apartments? (or any other arrangement of the above that makes sense for the local situation)?

The reason you think more transit will be needed is because you are assuming that separate business and residential districts are required. However there is no particular reason it must be that way. If you can get people within walking distance of work and a few stores they won't needs as much transit. Transit becomes what you need for rare trips.