I would imagine that there is caution about becoming beholden to user donations to continue operations. Such a situation would give users a measure of effective voting power in the development of the browser.
If you were starting a project from scratch I could see that as a valid concern, but the current world is one where 80% of the funds to pay for Firefox comes from Google. No one can seriously argue that becoming beholden to your users is a worse situation than becoming beholden to your primary competitor.
I don't think so, but close. I think they're indirectly paid by Google to keep Firefox around as a token competitor for antitrust purposes. I'm sure that's what the "search deal" is really about. Because Google already owns the search market, they don't have to pay for it.
However with falling marketshare there comes a point that when that won't fool regulators anymore. And then there's no point for Google to keep paying.
It seems more likely to you that Google isn't serious about Chrome's dominance than that they're totally serious about it and are using Firefox as a guard against antitrust and using their funding of Firefox as leverage to get Mozilla to cave?
That's the same situation basically any for-profit company with a paid product is in, is it not? If people don't like your product or don't see a future in it they will be less willing to pay for it (or donate for it). How is that bad?