Because they're stupid. The NHL has their own YouTube channel, and promotes fan made videos with highlights, in fact they've been known to play some. The Kings hired a guy to do highlight videos because he made great YouTube videos of them already.
NFL is just greedy and anti-fan it seems.
They can't see the obvious opportunity with the power of the Internet.
Imagine if they did a contest every year for fans. And the fan who made the best highlight video got a prize. Like sitting in the suite with the commish at the SB. Imagine the media coverage and hype that would surround that. Each team could even have a local winner that would get to sit in a luxury box with the GM or whomever.
Sometimes I think the marketing people at the NFL just rely on the radio and TV stations for coverage and don't bother with much else. Can you imagine opening up a contest like this to fans of every team. All 32 pick a winning video highlight, then each division has a face off and there are playoffs and then a Super Bowl.
It could be millions of dollars worth of free promotion and attention.
But they'd never think of it on there own.