Scarra loves to play Vel'Koz mid and he had a discussion with his chat about why Vel isn't seen that much even though this meta is, arguably, where he should shine. The following sums up what he said (although he only discussed Kog'Maw).
The major limiting factor is the existence of other champions fulfill a similar role as him (long-ranged poke/sustained aoe) but do it either more reliably or have more reliable aspects that makes how they fulfill the role generally better.
Vel'Koz competes, mainly, with Ziggs, Xerath, and Kog'Maw right now. Ziggs brings much more reliable waveclear/poke/AOE damage than Velkoz. It's hard to land Vel's Q in crowded teamfights, and his W requires enemies to stand on it to proc both instances of damage. Xerath is bugged right now which is why you don't see him that much but he is similar to Ziggs in that his damage is more reliable/easier to land. Sure, Velkoz has true damage to shred through health, but reliable damage is better than potentially no damage.
As I said, Scarra covered Kog'Maw vs Vel'Koz. His damage is also arguably unreliable, but once he hits 16 he's unarguably the best midlaner in the game because of how stupid his range becomes (which really makes up for its unreliability since its so stupidly spammable) and how hard it is to get to him if played well. There is just no reason to go with Vel'Koz when you can pick Kog'Maw and rush Luden's.
I think Vel'Koz is a fine midlaner to pick right now (and I love playing him!), but, when you are in a situation to pick him, and Ziggs, not bugged Xerath, and Kog'Maw are open, it is very hard to justify picking him over them.