No, I don't think it's a "must-have."
I've seen many a beautiful model finished with only spray cans and brushes.
I will say this, though: an airbrush sure is a lot of fun! Out of 30 years of modeling, I've only had an airbrush for about 4 years now. Can't say I've mastered the art yet, but I'm fairly happy with the results I get, and I can do things now that I couldn't do before.
So, is an airbrush a valuable, versatile tool that can help you create amazing models?
Oh yes!
Is it a "must have?"
Nah.
I had 26 years of very happy modeling without one!
Having said all that, I would't build a model without one now....
Ah, what a contradiction-filled post this has been!