Airbnb was iterating prior to being part of YC, they've given several interviews where they talked about how they'd gone through several launches and failed to take off and had to iterate on their model. For example they started out by only being an introduction service, but they found handling the payment in person was actually a major issue (socially awkward, no record of transaction, etc.) so the end up incorporating payment handling into their service. That was likely a critical iteration.
Google's primary business is Ads which wasn't what they started with.
Handling all payments is absolutely critical because it leads to a review/rating system that is credible (which is critical for a service like Airbnb where strangers are offering and renting space to/from each other). As soon as the payment processing is gone you end with a review/rating system like Yelp. Namely one this is easy to game (for example business owners offering free things to people who give them a good Yelp review) and therefore carries little to no weight. I've used Airbnb three times now. The credible rating system was crucial for me to feel comfortable staying with a total stranger.
Google's primary business is Ads which wasn't what they started with.