The problem is that he sucks. And since he's proven that he's not good and a major distraction because of the attention he gets for whatever reason (confounding because he's a bad QB), he's not an ideal backup. Why the heck would a team want a bad backup QB that gets tons of attention for no reason, even when he doesn't play?
Tebow has the lowest QBR of any quarterback with at least 30 games since 2010. THE WORST. The eagles have 3 of the top 5 worst QBs on that list. Mark Sanchez, Sam Bradford, and Tim Tebow. Hilarious.