Does the airbnb app or website even serve third party ads?

It's less useful to focus on this single example, and more on the industry. Once these types of ideas gain momentum, they just become to be accepted as truth.

"If everybody else pushes users to their app over web, there must be good reasons to do it, we should too."

Expecting companies to rationally analyzed whether that is actually the case, is, well, expecting too much of companies.