The original Halo port would have (probably) run on the same DX version between Xbox and PC.
It's one thing changing platform, but retrospectively updating the codebase to deal with 10 years of API development is a pretty awful task for any team. Many ports of old games to new systems would suffer from the same stupid difficulty.
Every game is a bit different, though. Sometimes you'll get things like Jak and Daxter,
which was written in it's own programming language called GOAL and had 10 different rendering engines.