Medicine without leeches.
If somebody wanted to set up a fair-use foundation, the music equivalent of a clearing house for donation-supported software, it would have some hurdles to clear. For example, one hurdle would be that 100% of the donated money got to the intended recipients. Another would be that the intended recipients be choosable. For each track, you could choose whether you wanted the donation to go to the musicians, to the technicians, to some charity, or to the label itself. We know in 2017 that this would not work, because the label executives always find ways to siphon off money. It's what they do. Expecting them to do otherwise is like expecting a rat to be tidy. So, would a government pass legislation prohibiting labels from siphoning or clawing back this money--and regardless of whatever weasel words are in the contracts with the musicians--with 3x damages and possible jail terms for the execs? Without that, the idea is a non-starter.
You'd need good ways of anonymizing donations, first that a person donated at all, and second which particular pieces were chosen. Otherwise, labels would try to convince gov't that fair-use donations were an admission of copyright infringement. It's absurd, but it would take only one crooked administration somewhere in the world to start an ugly mudslide.
So, for example, one might want to donate $5 for fair-use of The Beatles, Lucy in the Sky With Diamonds to the Timothy Leary Foundation (if there is such a thing, I apologise). On the credit card bill one would want it untraceable, and on the site, at its Lucy page, the donation would be credited to a hash code, which one (but not anybody else) could verify. For the untraceability aspect, it makes sense to me that the site fall under the wing of a large retailer, even though otherwise that makes me cringe. So it would show up on your credit card bill as a transaction with Orinoco, which nobody would question because 99.9% of its transactions are for widgets. Thinking out loud.