Different engines, and different visual compromises. If cheap large-scale shadowing without baking was easy in Halo, they'd do it.
Fully real-time shadow projection is always fairly expensive, and coming up with a system to do efficient baking in the background, assuming it's possible, would not be a trivial task.

What I do know for sure, though, is that many games this gen with "impressive graphics" would absolutely have a hard time targeting large-scale real-time shadowing, and it's something that the lighting engineers at both Bungie and 343i decided to avoid. Now, I'm pretty sure that you're not a lighting engineer, and I'm a kinda/sorta vaguely proto lighting engineer at best:

(This image uses spherical harmonics, by the way. Halo 3 uses spherical harmonics for its baked light maps. This approach is very precomputation-heavy; renders are pretty fast and have very good diffuse lighting, but it took about 1 billion spherical integral samples to set up the vertex transfer functions for just these two low-poly spheres.)