On the contrary, search ad revenue is but a relatively small part of Microsoft's overall business. If you want to place bets search is a critical battleground for AI (Microsoft/Satya clearly seem to), it makes sense to attack them here.
For google, search revenue largely is the business. Every point Microsoft can take out of Google's search marketshare hurts Google far more than the reverse. Attacking Google's browser share will also reduce the number of people with Google search as the default.
Forcing Google to adopt more LLM/AI features will also significantly increase their cost per search query in the near term, if Microsoft can meaningfully change consumer expectations of search. These LLM queries are much more expensive to service today than a traditional search.
This is all the more interesting because for the first time ever Google have wobbled in their dominance of search, there might actually be an opportunity here for Microsoft. That was almost unthinkable a couple of years ago.
I personally don't see how this is any better or worse really than the billions of dollars Google pay Apple every year to secure the iOS default search engine setting, eliminating vast amounts of rival marketshare in a single move.