You can. There are a lot of open source projects that solicit donations, and if you talk to the developers you will find out that practically none of them get donations that would support even a single developer.
The only thing that seems to somewhat work is Patreon, which seems to work fine for some developers that are good marketers, but even there the number of creators that can support themselves is very small, and I don't know of any Patreons that support more than a single person.
To support a browser, you need a team, and there is no plausible way to pay for that team with donations.
It's not that nobody has tried financing open source with donations, it's just that nobody has found a way to make it work yet.