I don't think the question is "can you be," the question is really, "Why would you *want* to be a football powerhouse when you are already an elite academic school?"
In our case, we have a very difficult reality: The UAA contributes a laughably small amount of money to the University itself. About $6 Million, which is a drop in the bucket compared to what gets added to the UF endowment every year through private donations. UF has a $2.0 BILLION endowment, (more than three times that of FSU) and the UF administration and board of trustees have a unified ambition to double or triple that very soon. The donors they are seeking are not necessarily people you'll find sitting in the football bleachers. Al Warrington has donated over $100 million to the UF endowment alone, mostly to the business school. Herbert Wertheim has donated $50 million to the endowment and it's been directed mostly to the engineering school. Believe it or not those guys aren't even big fish when compared to donors at other prestigious schools like Harvard and Stanford. Donors like these are industry titans and inventors. They want their names on buildings and schools, not sports facilities.
So our last two presidents have been focused primarily on building the endowment through private donations. The football program is a distant afterthought. Their biggest concern when it comes to football is some potential scandal that could bring disrepute to the University. An academic scandal like the ones at FSU, North Carolina and Auburn would be a setback to them and a hindrance to their fund raising efforts. We are adding $400 Million + to the endowment every year now and that number is expected to grow substantially. As long as the football coach isn't disgracing the University through scandal and keeps winning 8-9 games a year, everything is hunky-dory to them.
In other words, we have more in common with Vanderbilt than we do Alabama or Clemson. Not to be a Debbie Downer, but that probably won't change any time soon.