One way to look at this arrangement is that it would be an enforceable contract.
As a contractual matter, there is an agreement between you and the customer, and a separate agreement between you and the artist. In the first agreement, you have to give something of value, and the customer has to give something of value (money). You would be offering self-generated good feelings and encouraging something that the customer finds valuable. You would need to be clear about what they must do and what you must do, and assuming that, it would be a valid thus legal contract. (I set aside the question of whether the Spotify TOS might prohibit you from doing this: my answer is not Spotify-specific).
To be a real contract, you ought to be able to say what would be a breach of contract by you or the customer (you don't define breach in the contract, but conceptualizing the matter this way will help clarify the terms). You could breach if you simply refused to pass on the promised percentage, or unilaterally changed the percentage, or surprise customers by refusing to support Björk or Enya. The customer might breach by e.g. inflating hit-rates by some software means, or by paying with fake money (rubber checks, invalid cards, whatever). One thing you cannot reasonably do is promise that the artist will be cooperative, so your promise would have to be clear about the non-cooperative artist option. (Suppose a customer listens to Björk, Enya and Smith in that order, but Björk declines to cooperate: is the money automatically re-distributed to Enya and Smith, or does Björk's share go to the customer's charity? What is both the charity and artist are uncooperative – unlikely but not impossible?)
Theoretically you can also form a contract with the artist, where you give something of value (money) in exchange for... and that part is not clear. "Providing bank details" might be the thing of value (valuable because it enables your contract with the customer). But there is no obvious reason for you to actually form a contract with the artist, and it is legal to give someone money with no strings attached (though you may have to mind income-reporting laws, if you hand over a lot of money). The tax consequences of this scheme should not be overlooked.
Another way to approach this is that you are running a charity, serving as a clearinghouse. Charities are highly regulated: the Minnesota AG provides this guidance on some of the law. If one opts to create a charity, one should hire an attorney. If one opts to not officially create a charity but does something that looks like it is a charity, one should hire an attorney to figure out how to do this so as to avoid prosecution for operating an unregistered charity.
There is also the potential that this could become a money-laundering operation. The federal Money Laundering Control Act might be relevant. The entire thing as enacted originally is here (193 pages), the laundering part is Subtitle H. Fortunately, what is outlawed is willful acts, e.g. "knowing that the property involved in a financial transaction represents the proceeds of some form of unlawful activity", "with the intent to promote the carrying on of specified unlawful activity". Thus one should hire an attorney to make sure that whatever you do, you are insulated against money laundering charges.