I think a while back that was under consideration, but the spec-writers gave up since they knew that no matter what codec they picked, they knew they couldn’t get all browser vendors to implement it.
You're probably confusing it with Theora, which was actually part of the spec for a while but was removed around last June for the reasons you mention. That's when the public shitstorms started. I was an avid reader of what WHAT-WG list around the time leading up to that and I never recall anybody seriously proposing H.264 be put into the spec.
Ah ok. I didn't learn of the issue until after Theora was removed, so all I saw were the reasons why neither H.264 nor Theora were in the spec (and the impression that at least one of those had been considered for it).