I think it absolutely would be great if a Wikipedia-like model were viable, but Wikipedia is like the extreme high watermark for that, and they get five billion visits a month, which I think is an order of magnitude higher than what Firefox has access to. Ramping up to Wikipedia scale levels of donations would be a serious project and a significant gamble.
Wikipedia has also been around as long as the internet itself and its current fundraising drives are the culmination of decades of momentum and cultivating a perception of the compact that exists between them and their users.
Also, I believe that even in the best of times Wikipedia is raising about half as much as it costs to run Firefox.
There's probably important caveats that relate to comparing software development projects with resources and content, because I think the most successful donation-driven examples are Wikipedia, NPR, and The Guardian. And what they seem to have in common is generating content to be consumed.
In terms of software development projects, to me the most natural analogy is something like VLC, which does indeed rely on donations and is orders of magnitudes smaller. Or maybe the Tor project which does rely on donations, but I think they're at the order of like 10 million or so, which is certainly promising, but not a like for like substitution for the revenue they get from Google.