I think OP means they don't mind sharing their information with the search engine (be it Google, another engine that provides better results, or even a better Google in terms of results), _as long as_ OP has control over exactly what is being shared.
As an aside, I do see the trend for some companies to provide this control nowadays. Even Google is doing it (e.g. you can auto delete your information, or turn them off completely): https://myaccount.google.com/data-and-privacy
Of course, whether or not you believe Google is doing what you have configured in the backend is another question... and there is nothing anyone can do to actually make you believe it short of giving you complete access to the entire Google backend. Or is there a way to verify without exposing? Maybe an interesting research topic...
I don’t think Google taking your information and sharing it with advertisers is a great sin. Somewhat annoying but nothing particularly harmful.
I do think the search results are easily manipulated and it can be frustrating trying to find relevant information. Like most people I end up defaulting to Reddit for search queries just to find something that isn’t a blog by someone shilling their product.
But I understand the invasion of privacy would irritate some people and maybe in the long term it would be a net negative. So if there was a search engine that explicitly asked for certain information and you had the option to share, that would probably go a long ways.
