I find the draft unwatchable because of the timing. Plus, it seems like it actually takes more than 15 minutes some times, because the team only has to turn its pick before the end of the 15 minutes, and then there's often a delay before the next team gets notified of the pick and put on the clock.
But at the end of the day, the draft should be about the draft, not about watchability.
I think the same people are going to watch the draft whether it's 10 minutes or 30 minutes. And the reality is that either way, I'll just flip back and forth every hour to see the last four picks scroll by.
The NBA draft, by comparison, is extremely watchable. But it's a completely different sport. There, you're talking about essentially 80 guys fighting for 60 spots (and maybe 15 fighting for the top 10), and you know pretty much all of them if you like college basketball.