I think the question is not whether it is a F2 or smaller aperture, but rather it is a question of how fast the lens system focuses that will determine your keeper rate.
Canon came out with a book on their EF lens system, where they have described and compared the different lenses in terms of angle, weight, focusing speed, min focusing distance, etc. I suggest you get a copy and read it.
To answer your question, the key criteria for the lens to capture kids in action would be:
a) fast focusing speed
b) high fps
c) good timing and technique
It does not matter even if you use a f4 lens but it focuses fast enough so that you can get a high capture rate. In my experience, all the USM lenses focus extremely fast, some faster than others. I got best results with the 85f1.8, 50f1.4, 28f1.8. Even the 17-40f4 and the 小小白70-200f4 IS both focus with lightning speed, so the capture rate is pretty high. The 135L, 35L, should also be very good with different perspectives, either from a distance or up close.
Your 60D has a high fps, so the rest is up to you. Just use the servo focusing and continuous shooting and shoot bursts. Or wait for exactly the right time, and shoot a couple of shoots in sequence. For kids, its also best to get down to their level and shoot, not from the "adult" perspective, which is quite boring.
Happy shooting.