Auburn can win, but Auburn came pretty damn close to firing Tuberville shortly before he put together a 13-0 season.
Alabama wants a coach who can come in and immediately go 9-3 or 10-2, with some of those wins coming over LSU, Auburn, Tennessee, and Arkansas.
A good coach COULD do that, but it's very hard to do that year-in year-out and Alabama's fans have such high standards that it's easy to get on their bad sides.
Unless a coach is given a few years of stability to get their system and their recruiting in place, it's unreasonable to expect them to come in and knock off a bunch of perennial world-beaters like several of Alabama's permanent SEC opponents, which are Auburn, LSU, Arkansas, and Tennessee.
The recruiting isn't horrible. It could be better but it's still Top 20 in the country. Good enough to be more competitive then they have been.
What really bothers me about the "you can't win at this school" line of reasoning, you're letting bad coaches like Mike Shula, Pack Hackett, and John Blake off the hook.