If Thunderbird required users to sign up for an annual subscription, then that specific problem -- not being able to tell what good one's payment would do -- would go away. There would be a very specific reason to pay the money.

(In practice, they presumably couldn't do that, at least not effectively, because the code is open source and someone else could fork it. But let's imagine that somehow they could require all Thunderbird users to pay them.)

That doesn't, of course, mean that it would be better overall. Thunderbird users would go from getting Thunderbird for free and maybe having reason to donate some money, to having to pay some money just to keep the ability to use Thunderbird: obviously worse for them. There'd probably be more money available for Thunderbird development, which would be good. The overall result might be either good or bad. But it would, indeed, no longer be unclear whether and why a Thunderbird user might choose to pay money to the Thunderbird project.

Aside, they should. This thread is a good example of how groveling for donations distorts what should be a simple transaction.

Instead, people act like they're buying in to a 50% share with their $5 and then act like they cofounded the project forever after the donation.