There are other solutions that have been seriously considered or proposed. For example in copyright one idea is to allow things to be freely copied and have some rich entity pay creators. This was how it was done a long time ago, with the rich entity usually being a king or a ruler of a city-state or a wealthy lord.
Another idea is to pay creators via some tax on something that is roughly correlated with copying. An example would be a tax on blank tape.
A problem with these approaches is deciding who gets paid and how much. In the tax approach not many people seem to like the idea of the government deciding which artists should get funded. The usually way to avoid that is to have it based on how many copies are made. But then you need some way to get that data.
You could do it via some kind of polling. That was probably the only way back when copying was mostly physical, such as copying a record to a cassette tape. Nowadays when it is mostly digital you could do it by server side monitoring on download/streaming sites and/or device-side monitoring of playback--but then you are getting into areas that will worry many people for being an opening to more general surveillance.
For ordinary physical goods we don't have these problems--a free market (even the poor approximation of a free market that we have) works pretty good for determining what to produce. But that only works if the goods have certain properties, which copies of art do not have. (If anyone wants more information, look into excludable vs non-excludable goods and rival vs non-rival goods).
The approach of current copyright law is to legally give copies those properties so that the market can determine what art gets produced and how much the artist makes. This is a tradeoff, because it does mean that the consumer pays more for copies than the "correct" free market price (marginal cost of copying).
The other approaches mentioned above tend to make the tradeoff the other way--the consumer pays marginal cost of copying, but less art gets produced than consumers would like.
There's not really any way to avoid having either underproduction or underutilization when it comes to easily copyable art. Once you realize this things make a lot more sense.