I think long snapper is a really interesting case study of special teams and roster building. As fans, we talk in frustration every single year about "wasting" a roster spot on a dedicated LS. Yet across the league, the LS who takes meaningful snaps at another position has gone the way of the quarterback/punter. The last I checked, every single team in the NFL carried a dedicated LS.
The long snappers who at least nominally play other positions are generally either linebackers or tight ends. (Despite the fact that they both snap the ball, long snappers today aren't backup centers; their responsibilities after the snap are very different, and they have to be a lot more mobile.) A good example is 6'4" 250-lb Zak DeOssie, who was drafted as a linebacker but ended up earning his roster spot at LS, ultimately giving up the charade that he was still a linebacker at all:
http://www.nj.com/giants/index.ssf/2010/08/giants_zak_deossie_makes_trans.html
So let's say that a tight end like Ott can earn the LS job. What does his versatility get you? Does it save a roster spot? Probably not. I don't think anybody would be comfortable with just a rehabbing Gronkowski, Hooman and Ott at TE, so he'd be TE 4 -- a role they probably wouldn't otherwise carry. And they have to activate him on the 45 every week even if the TE's ahead of him are all healthy and vastly superior at that position.
Finding an NFL-caliber LS who is also a strong enough LB/TE
and a good enough fit for your scheme that you'd want to give him a significant role in your offense or defense is a tall order. It seems to me that the likeliest route would be to train an existing backup LB/TE to long snap. But if it were even remotely easy to do that, somebody would be doing it!
I can only speculate on why it's not feasible. Maybe long-snapping is a really specialized skill that most players can't master. Or maybe it's too hard to perfect that skill when you have to squeeze it in around full defensive practices. Or maybe teams have found that they need their LS to be available for so many practice reps with the punter and kicker that they can't spare him for offense or defense. Regardless, the entire league seems to have decided that LS prowess takes precedence over versatility.
And given the incredible havoc a shaky LS can wreak on a game, I can understand why.