wouldn't this just lead to the projects that are already the most visible (and thus most likely to already receive donations) getting the bulk of the income?

This could also result in low effort PRs, similar to Hacktoberfest

The donors should be able to preallocate a proportion to a list of preferred projects, and the distribution within those preferred projects may or may not be based on usage.

Then the remainder can be distributed purely on usage.

The reason this hasn't quite worked out in practice (although there have been many attempts) is because it is a difficult problem to solve without letting a bunch of abuse through.

With the specific idea of "paid per commit" is that people will abuse it because number of commits (or commits at all) is not a good measurement of if a project is valuable enough to get a portion of the donations.

Someone who has "finished" a project that is used by a lot of people and the maintainer is answering forum threads / issues from people wanting support sounds like a project that should have a portion, but if we only measure commits, they wouldn't in this case.

Another one who only does minor commits that doesn't really move the project forward (or even move the project backwards) just in order to get a portion of the funds without providing value, we probably think shouldn't get a portion. But again, measuring by commits, they would have.

So, difficult problem to solve, and whatever you measure it on, has a chance of being abused.

welcome to managerial theory

"What we need is a system where we can all pull from a common pool of FOSS donations. For example if my projects were registered and I made commits during a donation cycle, I could receive a fair portion of donation revenue"

That would be too gameable... it's too easy to make a million commits that provide zero value.