how about making an app that just stores the .tex files, and to convert them to pdf or something, the .tex file gets sent to a server
Putting it on a server makes the architecture more robust against messy code (and changes in programming languages and environments), because pieces can be changed independently.
The problem is roughly equivalent to producing a non-upgradable perl. It's not very useful on its own, but it's completely impractical to include a copy of the entire CPAN with it. And Apple's policies prevent you from downloading additional packages. It's just not worth the effort.
It does not solve the problem of writing TeX on an iPad offline, obviously.
Yeah, that's what TeX does.