In the most literal sense no, but I think it does address your point.
Honestly it’s an odd example to pick because there are paid firefighters too - why would you need to pay firefighters if enough people are willing to do it for free?
"How come volunteer fire departments exist?" is a rethorical quesiton. Whether volunteer firefighters have other jobs is beside the point. Clearly, useful tasks can be executed without a work context.
The reason you need to pay firefighters is because society is work-centric.
I think people would volunteer. Main reason not many volunteer is because they are busy with work. In a workfree society people would have much more free time to spend than they have now.
