Check your numbers
1) Penn State and Ohio State have more wins than Alabama as well. Check your numbers.
2) Pre-1936 polls are retroactive in nature. Take away a couple national titles. I see you noted they were "unofficial". By the way- this also takes Michigan out of the argument.
3) I don't see the coach argument. Every prominent school has at least 1 great coach. ND might be the only one with more than 1. Michigan had Yost (again, retroactive national titles) and Bo never won any. Florida State has Bowden. Penn State has Paterno. Ohio State MAY have two (Woody, possibly Tressel).
4) I don't see the player argument, at least not during the last 20 years.
5) Culture and Tradition?? This is complete opinion. Lots of great programs have lots of great traditions. I can't equate them. I can't say that one is better than another.
6) If Alabama breaks out with a title this year, they have a great argument. Otherwise, I think they have a historic argument only. Let's face it: We're 16 years removed from their last title, and 29 years removed from the one before that. Other SEC teams have seen multiple titles since that time. Where's Bama?