I'm not sure there is an alternative. It's not just Firefox: other big projects like this already have foundations and lots of money in funding, but then spend the money on things not at all related to the core mission.
From what I've read, Mozilla won't even take your money to develop Firefox. They'll instead use it for the Mozilla foundation which funds a bunch of social causes.
Wikipedia has a huge endowment, so they really don't need money to keep the lights on, but if you donate, it'll similarly be used for funding social causes through the Wikimedia Foundation.
There's also a Linux Foundation for funding Linux-related stuff, but here again a lot of it is spent on social causes, not directly on development-related costs.
You'd think that if funding were really that tight, social causes would be cut and just keeping the servers running and essential personnel employed would be the highest priority, with SW maintenance and development a close 2nd. So, apparently, money must not be that tight. Or, if it is, it's being woefully mismanaged. But I think there's more to it: it seems like when times are too good (something gets popular and gets funding), then the people in charge expand the scope of the project to consume all the funding, adding on various pet projects (like those social causes), instead of saving the money in case of a funding downturn later. Wikipedia probably did it best by setting up an endowment so that everything else is just gravy, but even here they're constantly asking for more money on the site and acting like they really need it when they don't.