You keep stating the obvious, we all get that athleticism matters. Programs develop that athleticism better than others. Being on the right stage matters. Being in the right place with the right coaches may help make a 7th round pick a 3rd round pick, or getting the right spot light may move someone to 1st or 2nd round pick from the 3rd.......the dollar figures vastly different.
If you just want a shot school may not be as big a factor. If you want a better shot at a real opportunity schools do matter.