OS X actually does this now. You get a little pop-up when you hold down e(èéêëēėę) for example and press a number to choose. It's efficient enough if you don't type them often enough to remember the alternate keystrokes. (option something something)

It actually doesn't work well in TeX because it depends on having the correct input encoding set, which still breaks when you have multiple collaborators. Though \:e for ë is pretty easy to remember.