Technically with moves like this, we already are. The question should instead be phrased: would enough users opt into giving money instead of being advertised to, and that's much trickier. You'd lose some opportunity cost with an ad or not model and having to support that, but I think a nontrivial amount of people would rather spend money than be advertised to.
I pay for two newspapers (WSJ and a local one) and I am still served ads in both. My local one still serves "sponsored content" which I consider to be the worst kind of ad. WSJ also seems to have no problem with using targeted ads and third party data collection. I understand why they do it; I'm the kind of person to pay for a newspaper and that makes me an especially valuable.
I genuinely don't think it is hyperbole to consider online advertising perhaps the single most destructive invention in the last decade and a half. Many of the terrible aspects of social media would not exist if people were paying for it with their dollars. Social media has exasperated divides and now poses a serious risk to democratic institutions.
Anonymous trolls in a no advertising world would be fewer because people would actually have to pay for those twitter accounts. Moreover, there would be no incentive for online publications to feed us clickbait, sponsored news, and outrage simply to encourage more eyeballs on ads.
While WSJ comments can be pretty partisan and terrible, they pale in comparison to Twitter's.
There are definitely enough users who would donate money to support a fork of a browser that pursues their interests. Not enough who would support Mozilla though.
Unlike most other software browsers are in a unique position here. They have regular users that use the software often and a lot and can do periodic donations campaigns that reach all of them. On top of that there are billions of potential users opening various niche possibilities. This may not be enough to develop a massive full blown browser engine, but definitely enough for forks.