Most users will probably switch to Google anyway, at least in the short term. Google will probably lose some market share. This means less revenue. However, the "cost of revenue" is lower as well. So it may just be a wash. When tobacco companies were banned from advertising, their big expense of advertising went down as well - and so profit rose. Google's long-term outlook looks murkier. It really is possible for new entrants to come in and steal market-share if they didn't have to pay for default-privilege. Platforms could encourage specialized search engines as well - pick one for shopping, another for maps, another for reviews - maybe we'll get a Cambrian explosion?
But the fact that no ad-support search engine has been able to beat Google all these years, even Microsoft-supported Bing - means that internet search is fundamentally a hard problem to solve. It's also relatively capital intensive - all the hardware to crawl and index the web, human SERP raters and content moderators.
As the internet becomes more and more hyper-commercialized, the value of a general purpose search-engine may decline. Why search when there's mostly garbage out there. Try going to any news website.