You raise some interesting items for discussion, though this thread is about a specific meeting at Stan Con tomorrow (it will be 1-2pm btw). That meeting is about stanc3 compiler optimizations, which for the moment doesn’t do much w.r.t. Eigen or anything specific to the Stan Math backend.
I’m confused about what you’re saying and you may also be confused about what Stan is doing under the hood, haha. Take a look at the autodiff paper, I think it’s the best source on some of this but it also doesn’t talk about everything you mention. For the rest I’d suggest starting a new thread about the Math library and algorithms