Most free open source projects are hobbies, not jobs
Do you think that is a good situation?
As such, the goal of devs is often (and should be) to deliver a good product to people, no strings attached
Why "should" it be the goal of the dev? Who are you to decide that for the developer?
Expecting revenues with this project will slowly move you towards the non-free open source projects category
That's a prediction and I don't know what data you're basing that off of. Could you share it?
I would imagine if a search engine is willing to sponsor a project in a way, then it must make enough money to justify that, and that often comes with bad privacy. I guess the default is Bing or something? The revenue comes at the expense of users on the default settings.
Those are all assumptions. You do not know if the search engine is making enough money already. They might be trying to make money in the first place and getting it in front of users might be a way to raise awareness popularity. There are also companies like ecosia, duckduckgo, qwant, startpage and others that do care about privacy. Would you be against their sponsorship too?