At one point in the past I heard Booking was the largest spender, worldwide, on Adwords.
I wouldn't immediately consider the hotel metasearch products a problem for booking. It shifts traffic to different paid channels with different tradeoffs (eg. less fine grained control of spend if it's a revshare model). I ran the product development in marketing for a little while. Some years ago (ie. late in the game, largely due to politics), we started investing in cross channel attribution models to better direct spending.
Disclosure: I no longer work for Booking, though. I do work for Google, but am in NO way involved in Ads or travel and an not trying to comment on the company's business.
Seems like Booking and Expedia disagree with you:
https://www.marketwatch.com/story/some-of-the-biggest-tech-n...
Time flies!