Well, think of it as freelance work with a company. With that you invoice your client and they pay either within 30 days of receipt or at the end of the month. (Obviously that doesn't apply to your plumber or decorator fixing stuff in your home - you usually have to pay immediately - but I bet it does apply when those same tradesmen work for a company.)
The alternative is to be paid cash for the gig but risk being stiffed for part of your fee with some stupid excuse (not enough people in the pub, etc.) or be asked to commit fraud by signing a receipt for a higher amount than agreed so the landlord can pocket the difference.
So there are two reasons why this is happening - accountability and, as you mention, the slow death of cash. You almost need a mortgage to buy a round these days, you have to use plastic...
As long as you keep track of the band's finances, the system should work. 👍