The short-term rental market is much more mature now than it was at Airbnb's founding. There are reputable management companies all over now with their own platforms, payment gateways, reviews etc.
Literally all of the lodging management sites that take a cut of transaction have this potential issue, and they've all figured out how to deal with it. It's a solved problem.
I'm curious how Airbnb specifically is solving it. I can think of four bookings off the top of my head--expensive ones--where they've missed out on my money because the hosts solicited offers to circumvent the platform. It's worked out fine for me each time.
First, AirBnB will kick hosts off the platform if they find out.
Second, as another commenter mentioned, many customers appreciate the support and guarantees paying through AirBnB gives them. All it takes is one shitty experience or getting scammed for folks to think twice about going off the platform.