I'd prefer the chase mechanics to work for any sort of chase, rather than just be vehicle based. I'm also a bit unhappy that our current ideas for chase mechanics so far are just 'roll drive (or athletics, or whatever the chase skill is) until the chase is resolved'.
Of course, the problem with allowing you to use 'other skills' during the chase means that most people will attempt to apply whatever their best skill happens to be. The same problem cropped up when discussions were ongoing about how to make a skill challenge system for DnD 4th that actually worked.
Yeah, just using the one Drive skill is not so great. However, we either need to expand the skill list so there's multiple skills you can take and use in a chase, find some way to add tactical depth on top of the Drive skill, or figure out what else we can roll.
I'm not a fan of the first option unless your campaign is all about chases, then by all means, tweak the skill list.
I think the second option is a laudable goal no matter what we roll.
But I think the third option might have merit, at least for vehicle chases: Vehicles have skills, and you roll THOSE. You can modify them with your Drive skill, but the skills come from the vehicle. Alternately, the vehicle stats act as modifiers to your Drive, either in the sense of restricting/complementing or as actual flat modifiers (+3, -2, etc). Either way, you can end up with a range of different stats that you can roll on, and those stats don't need to unnecessarily complicate characters outside of chase scenes.
I like Speed, Handling, and Body:
Speed: outrunning pursuit, acceleration, drag racing, maximum velocity
Handling: cornering, driving the wrong way through traffic, avoiding collisions, braking
Body: surviving collisions, ramming, passenger protection, plowing through obstacles
See, now cars can even have Stunts like "Cut Off", where you move the "ramming" trapping from Body to Handling, or maybe "Boxed In", where Body gets used for the "cornering" trapping.