With the exception of removing the "Leader" role (in the context of 'healer'), I doubt you'd see much, if any, change. The tank/"Defender" would be focused on soaking and/or dodging damage rather than ablating it, and the "Striker" and "Controller" would be largely the same.
The biggest difference is that gameplay, as in True20, would become much more random, with virtually all attacks taking the form of 'Save or Die,' and one of D&D's main strengths, its ability to appeal to a wide variety of players, would completely disintegrate. The game would cater exclusively to one narrow splinter of Simulationists, those who want to attempt to 'emulate reality' (as they see it).
HP work. They work better - MUCH better - than anything else anyone has come up with in thirty years, and that's something I can't say of ANY other element of D&D's original design. They work so well, (electronic) game companies whose development budget for a single A-list title is comparable to Wizard's ENTIRE budget and who have the data-collection resource to put that budget to use almost exclusively use hit point systems. In fact, HP work so well, they're now almost UNIVERSAL in electronic games, and the old one-shot = one-kill rules all but completely abandoned.