Brief thoughts - don't let me interrupt the conversation (mainly cause I like what's happening here).
Of course, that makes perfect sense. But in game terms wouldn't that be increasing Strength (ie. one aspect of general fitness) which is useful in all three disciplines? Rather than learning skills & techniques for a specific purpose. For instance, learning backstroke isn't going to help you wrestle somebody to the floor. Knowing Judo doesn't help with abseiling. Other than the generally increased fitness level that accompanies continued pursuit of these activities.There is a measure of athleticism that goes with both judo and rappelling, and if someone is notably good at Judo, they're unlikely to injure themselves abseiling.
See, that says to me that Judo has nothing to do with abseiling necessarily- but rather that the guy good with Judo and the guy good with rapelling both share some root characteristic (such as being strong). Being good at one doesn't make you good at the other, but being strong is a trait common to people who are good at either one of those activities.
There is a measure of handwaving that goes into all skills, and I would just as soon not see Athletics become another focus skill.
Basing Grappling on the Unarmed attack bonus would tilt the fighting field even more towards the combat characters and eliminate a relatively easier way to boost a social characters combat effectiveness.
See, that's not a situation I see too often. Barring Origin skills, there are very few characters who have Athletics and who are not good at fighting. Certainly, there are almost *no* social characters that get Athletics as part of the core skill package (Assassins, Courtiers, Emissaries, etc.). The logical correlation between "swinging a sword well" and "being physically fit" is just too strong in many cases.
Where I have some concerns with an Athletics-based wrestling system at this moment is twofold:
1) Characters who don't have Athletics are f'ed in against an even moderately Athletic character. Totally.
2) Characters who don't have Athletics and whose players know they'd be f'ed in grapples effectively have to burn an Origin skill in order to survive that deadly corner case.
Something like BAB which increases over level in our system means the guy who "fails to play the game right" has a chance when he's grappled the first time - he gets a slow climb up the BAB ladder as a social character, while the guy with Athletics can't quickly outdistance his natural BAB progression using skill ranks.
I think it all comes down to how deadly you think Grapples should be. Basing my opinion totally off cinematic expectations, I think "not really" - interesting, without a doubt; accessible, yes; inconvenient, yes; ending with one guy in cuffs, absolutely. But character-ending? No.