I don't think the 300/4.5 ED AI Nikkor is that well suited to sports based on my ownership of the 400/5.6 ED AI and previous ownership of the 300/4.5 AI (non-ED). The focus is slower than the IF manual focus versions and drags as it is focus close. I lift the front of the 400/5.6 ED AI and used to the 300/4.5 AI (non-ED, non-IF) with one finger to cut the drag. Any other use and the ED AI (non-IF) version are said to have better image quality. I can only repeat what I've read because I've never owned the 300/4.5 ED AI, though I would like to and I've never owned the 400/5.6 ED-IF.
I think those advising more modern lenses are right but then I haven't owned any of these AF lenses. I would think this advice holds for sports and wildlife were rapid and accurate focus is very important.
For sports consider focus speed and accuracy of focus. It doesn't matter how sharp or how well corrected a lens is if you miss the focus.
One more note on the 300/4.5 ED-IF AI/AIS. The focus is very fast so it may have a lower reputation than it might due to focus errors. It takes skill and practice to nail the focus repeatedly. I trust the 300/4.5 ED-IF can't attain the image quality of the 300/4.5 ED AI (non-IF) as the non-IF lens doesn't need a IR focus index mark.
I've used Nærfoto Bjørn Rørslett (the legacy site) as my Gold Standard for lens reviews. I've bought several lenses based on those reviews and kept one I might have sold.
Hope this helps,
Dave