The main and i think the only one benefit is that you (your clan) will have a board. If you want, after you became official you need to wait 6 months and after you pay, if you want 40k and you will have your private board.
all it proves for your clan is a clan board and the fact that you spent 50k on a square bracket change and a clan-specific board to talk in, which is almost never talked in.
Sense of accomplishment for the members of the clan is another thing which wasn't named here. The board is the big element, but knowing you guys did good is a big reward!
If you become official I will also draw you a picture of whichever animal you want.
Just if the benefits already mentioned didn't motivate you enough.
But yea, if you're serious about your clan I'd recommend trying to get official. Most of it in my opinion is just knowing that the council has faith in it not falling apart immediately.