You are actually being too kind when you say that there isn't any excuse for them to be trading titles with Saban because you limit their underachievement to just the last 10-15 years. You can go back way further than that.
The SEC's featured, dynastic program really should be Georgia, not Alabama. I don't mean over just the last 10-15 years, I mean as long as the SEC has existed. Georgia is in a better location for recruiting, is in a wealthier, higher population state, Athens is a much better city than Tuscaloosa, and UGA is a better school than UA is. If any SEC school is going to have 18 claimed national championships in their history, UGA is actually the school that is set up the best for it.
The only thing Georgia has been missing over the years is coaching, and arguably they have missed on coaching because the lack the commitment to winning that others schools in the conference have. And IMO, it affects their entire athletic department. UGA should be even better at football than they are, but that certainly isn't to say that they are bad at football because they are not. However, UGA on a near year in/year out basis should also have very good basketball and baseball teams. There is incredible basketball and baseball talent that comes out of the Atlanta metro, and UGA either doesn't develop it in those sports or other schools come in and get it.