Google Search is still a large fraction of Alphabet's revenue, and Alphabet needs to be able to deliver AI results for people's searches if it wants to stay relevant in the search game.
I imagine it's much easier to have fine grained control over AI search results if you develop and own the AI yourself.
Last I checked their AI results were terrible, worse than anything I get from ChatGPT or Claude. The only benefit is their AI results are fast.
If I were google there's no way I'd leave their AI overviews in place as-is.