[friendzis]

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.

[HPsquared]

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

[friendzis]

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.

[brewdad]

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