> this might easily change
This is a perfectly testable hypothesis in the free market. You can start a museum and market it, and see if you generate a profit. If you don't, then you have to fund it yourself (pay) or hope a handful of others value it and pay.
> often without any direct money involved, e.g. around church or school
There's much money involved in organizing people and having venues for whatever it is they do inside those venues. In these cases, the people paying for these organized singing events are what you would consider a patron. Churches and schools aren't free.
Modern instruments cost a lot of money, lots of labor to produce.
As far as just some friends getting together and signing because they enjoy it, that's obviously free. But it's not a service that someone else is providing to you, that's just something you're doing because you feel is has value. What would be more analogous would be having a civic center where people perform and.... people pay money to enter the venue and be entertained.
Some people greatly value libraries and museums. I don't. Those people should pay for them. If from time to time, I might want to use their services, I would gladly pay. If there was a membership required, perhaps I would enroll if I felt the cost was worth the benefit. This happens every day for many other industries.
Anyway, the root of the point was that people don't value librarians so they don't get paid as well as programmers. This is true. If it wasn't true, they would be paid more. I know this really hurts the socialist sensibilities of people on this site, but it's the cold hard truth.