I primarily shoot portrait/fashion or sport (daylight - triathlons). I am a newer photographer, still learning.
While I like the 70-200 F4 I have lost some shots because of non-IS with the sports.
I shoot a lot of sports (my kids). Outdoor - soccer, track, cross country.
The keys to getting a sharp photo are high enough shutter speed, and the AF capability of your camera & Lens.
I have a 70-200 f/2.8 IS (mI), and I have to turn off the IS for sports shooting. Camera movement confuses the IS some times, and I get more keepers with it off. For sports, IS is of no use. Your 70-200 f/4 should be fine if you have decent light. Try bumping up the ISO if it is cloudy and you aren't getting the shutter speeds you need. Light room does a decent job of getting noise out, so I find a higher ISO is a good trade-off in poor light situations.
I have a 24-105 f/4 and I shoot soccer with it and it is amazing, very sharp, good AF.
A 7D is decent up to 1600 ISO, and the AF is really good. It took me some time to learn the different focusing modes, but once I did, it works very well.