So what I'm interested in is not how other people handle it. It's: do you think I'm right about WotC's intentions?
I think you are spot on. From what was shared at D&DXP, it really sounds like your PC doesn't have intimidate. They have perhaps a background that helps them with checks to influence people through force (this may actually use the word "intimidate", but there is no intimidate skill). And, you have your ability.
First, I do agree that this is a move forward (while having a retro feel). You are freed up from a skill list, but you sort of still have them through your background/theme/class/whatever. You are a gladiator, you know how to threaten. You are a merchant, you know trade routes. That sort of language takes us away from the roll and better encourages us to role-play.
Second, it gets us past the issue of the barbarian that can't intimidate because he isn't charismatic. Because you describe what you do and the DM and player get to collaborate a bit, your description can really get us back to a strength or con or other ability check for intimidate.
Third, if we go back to early L&L columns (assuming they keep this) where they described caps and minimums, it could be that the really great description by the barbarian on how she is crushing the chair against the wall, coupled with the really awesome strength score, all means you don't even roll. You just keep on role-playing.
That's all massive win for me, and I'm a guy that loved 3E skill lists.