Should a tuba be in a jazz band?

Yes. It depends on the style they play.

Sure.

While there are a few standard jazz setups, nearly any instrument can be incorporated.

Why shouldn't it be?

Only if you're desperate.

Otherwise, a tuba doesn't belong in a..... "Jazz" Band.

In classic back-in-the-day New Orleans jazz, tuba was the bass that could be heard over the other horn players. 

no.  but a comparable instrument might be a bass trombone if you can learn to play that.  

They are often called "oom-pah-pah" bands, for obvious reasons. And I imagine you actually mean sousaphone. The tuba is another beast.

In the early years of jazz, it was the principle bass instrument. The advantage is unlike a string bass, it's portable. I’ve seen a bassoon in a jazz band, that was weird.

Edit: Perhaps it’s the sousaphone that is more common. It’s still a portable low register instrument used before amplifiers.

Ever heard the Dirty Dozen Brass Band?

I don't see why not - why should string instruments be the only ones to play bass? Tubas are pretty common in trad jazz bands, but they feature in more modern ensembles as well.