You can say there is no getting around it but I have actually taken photos side by side of the same subject and the 70-200 were much, much better because of the difference in noise even with the crop. This wasn't theory only, but it was practice. The difference was the difference. Those two tennis photos are from a day when I had both lenses and I would shoot a player with one, then swap and shoot the other same subject, same location, same light. At the end of the day the 70-200 shots were vastly superior.You need to watch the video I linked to. If you are doing significant crops, then you are losing isolation and gaining noise. If it is just small crops you may not notice the loss of isolation or noise, but significant crops you will. Watch the video, it is all explained and demonstrated. A cropped 70-200 to 400mm will be the same DOF as a 400mm f5.6 lens and have the same noise as double your ISO. There is no getting around this.
I would never use my 70-200 f2.8 over my 180-600 for birding (unless it was in a cage or VERY tame!) as it wouldn't be able to pick up the bird's eye for a start, but the resultant crop would be worse. That is the very reason *why* these longer lenses exist, in order to make focusing easier, to make the resultant image IQ better. If you are looking for better IQ at that distance, then you need to invest in a better lens like a 400 f2.8TC, this is the price you pay for wanting great IQ and focal length. Using a 70-200 f2.8 in order to try to achieve this is destined to fail.
And again: not every photo is supposed to be a close up. Whether I'm using a 200mm lens or a 600mm lens, I'm going to want a field of view for many shots which would make the subject "small." Here is one of the most popular shots from a recent game:
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This is exactly the composition I would want. Any more zoomed in and it's just not the same photo - but these kids are small enough in the frame that the tracking is behaving in the difficult way I've been describing here. This was on my 180-600 at 180mm. I could have zoomed in and gotten a better chance at better focus tracking, but at the expense of not getting this photo. In fact, if I'd had the 70-200 on for this shot it would have been even better because the depth of field would have been much more shallow.
So yes, a longer lens can make a difference, but there is a certain level of zoom here where I am struggling to get the camera to maintain focus but which is exactly as zoomed in as it should be.
I'd also say this: I'm the only photographer (and I'm talking about professionals, not parents/whatever) I ever see at any of these games that even brings a longer lens than the 70-200. I come with the 180-600 in a backpack and occasionally swap to it. The other professionals are always just carrying a camera with a 70-200 on it. Obviously it is different at pro-sports games and college sports games, but this is the norm I see for high school sports, at least around here.