"Defeatist and unfair" are bizarre ways to describe it, but I'm not sure how the earmarking process would work: what would prevent Firefox from ostensibly allocating your dollars as donated to Firefox and shifted unconstrained dollars from Firefox to another initiative, with your donation ending up funding non-FF activities relative to the counterfactual? Barring the narrow case where they have more FF-only donations than unconstrained ones, this just seems like an accounting fiction.

To some extent it is, if they have other sources of money. Yes, if there's $N in the donations "for Firefox only" and the budget they planned to give Firefox based on other sources is $X, X > N, then they could keep the budget at $X and move the now free $N to other purposes.

But it can be made more complicated by that, depending on the organizational policies, levels of transparency, and funding methods. If, for example, they have an internal fund labeled "for Firefox", I'd expect $N in donations to go there, and would be pissed if less money appeared. Alternatively, if they were running a funding model of "$X for Firefox + money from donations", then I'd be pissed if Firefox was getting less than $X + $N (this would be equivalent to the recent "companies are stealing tips" dramas of share economy).

It's worth noting that charities handling multiple causes usually solve this by creating separate accounts for donating to each cause.

This ultimately can get as complex as Mozilla would like, but Mozilla has also a perfectly valid option of not allowing donations for specific purposes at all, and I think it's fine if they do that. Donors have no right to force Mozilla to implement earmarking if they don't want to.