> Google care very much about the complete and utter ubiquity of their search.

Google doesn't even need Mozilla to increase/maintain their search market share. When Firefox's default search engine was changed to Yahoo! in the U.S., many users switched back to Google [1]. Also, people who care about privacy use things such as DuckDuckGo anyway.

[1] https://searchengineland.com/report-yahoo-search-losing-fire...