What if someone is obsessed with heavy machinery, wants to try operate them for fun and maybe make a couple of pounds as a bonus?

Minimum wage laws are there to prevent exactly this scenario. It is deemed better to let inefficient enterprises that cannot pay even minimum wage to implode and support unlucky people via government programs rather inefficient enterprises.

On the first point - why not indeed? Why ban unproductive work?

Some companies pay minimum wage because they cannot pay more. Some companies pay minimum wage because they can not pay more. Once you allow the latter to pay less - they will, in a heartbeat. And policymakers do not want that.

No one is banning unproductive work. You still have to pay for it though.

What if some child wants to work in the coal mines? What if some worker wants to be paid in company scrip?

Unravelling worker rights is just a race to the bottom.

That's called not having a minimum wage.

Are we just now rediscovering why minimum wages are bad?

None of the Nordic countries have a statutory minimum wage, btw.

Edit: Any skeptics don't have to trust me, they also have the option to trust the International Labour Organization:

https://www.ilo.org/global/topics/wages/minimum-wages/settin...

We don't have a general minimum wage in Norway, because we don't need them. We have strong unions that have given us good tariffs for various industries, that acts as a minimum pay for that sector.

But there are some sectors (building, cleaning etc.) that do have a government set minimum pay, because they often would exploit foreign workers.

Actually, our foodora bicyclists a while back formed a union, striked, and got a tariff deal. So got rid of some of the problems around their gig-work.