I didn't say there's no skill involved. Obviously a slow GM will beat a fast Expert most of the time in bullet, but I think the skills gap just changes in favor of the speed player. Take a 2000 vs a 2200 in a G-45. Probably 9 times out of 10 the 2200 will either win or draw the game. If it's a bullet game instead and if the 2000 is just physically faster at moving, then I think the outcome would look closer to 50/50. An opposite way to test the skills gap, in my theory, is to play Fischer Random chess (though I don't play it really at all). That will weed out people who are strong solely due to their book knowledge of chess and focus more on those who are innately strong. In all, I prefer just regular chess under longer time controls.
How do I get past 2310 Bullet?!?!??!?!?!?

But yeah, speed is part of it. It can boost your rating 100-200 points probably.
For example if I had to play with a mouse that was a very different scroll speed, then I'd lose every time scramble.

Yeah, it's important to practice. If you don't play bullet often then your rating would go down. If you don't play at all, then it goes down even more.
I don't think that's hand speed though, more like thinking shortcuts that you have to practice. For example calculating very short and very forcing variations all the time. You never get to practice that skill in regular chess where it's more important to be accurate (not all variations have very forcing moves) and to calculate more deeply.
And I'd say if anything I'm a little slower than I was when I was ~1500. I think part of that is just due to age. I used to be able to move pretty ludicrously fast.
And I don't think a GM would beat an expert most of the time... I think it would be pretty much 100% of the time (if they're both experienced bullet players).
If it's a 70 year old GM who never plays online, then sure, maybe he'll suck so bad at bullet his rating would be 1500 or something because he can't make it to move 20.