I don't like the situation either, but I find it hard to blame Mozilla for not pushing monetization hard enough. I can't think of anything more I'd like Mozilla to actually do.
I'm rather against being sold out, and suspect most Firefox users feel similarly.
Offering services essentially entirely separate from Firefox could work, but comes with substantial risk. Mozilla will be more trusted than some fly-by-night startup, at least among the techie crowd, but also can't just burn investor money and start over until something sticks. (Ironically, the only thing that comes to mind here for me would be a privacy-oriented email provider.)
The only maybe, theoretically, kind-of, plausible route I see working would be more of an open-core-esque model, where their paid offerings essentially implemented extension-like capabilities that would benefit substantially from deep integration with the browser. Think things that would otherwise be impossible with the extension API, or have substantial performance improvements if only Firefox internals could be messed with.
But. So many buts.
I'm not even sure their organization is setup to allow this kind of thing. I'm sure their codebase isn't, especially if it might require special considerations to comply with their charter.
Mozilla would also gain a bunch of perverse incentives to restrict or cripple base Firefox, which would bite them every time they added a new paid offering. For example, just how much more flack would they have caught for the new extension API if their own offerings wouldn't have to abide by any of those new limitations?
And it seems inevitable that they'll have to spend some serious effort to minimize the amount of browser fragmentation issues that would now occur within Firefox itself.
After all of that, the extensions most likely to get me to buy in - literally and otherwise - to the whole concept, would be ones that would seriously strain Mozilla's relationship with Google and many other companies. Things like deeply integrated ad-blocking and other privacy-focused features would be most likely to get me to not only accept the practice but even spend my money. But step one of weening themselves off Google's money probably shouldn't be "Burn bridges with Google."
So... yeah.
What else is Mozilla supposed to do? I'm not overly enamored with Mozilla these days. Increasingly I feel I'm sticking with them less because of anything they've done, and more because of what Google's done. But still, I find it hard to blame them too much for treading water.