Dave W wrote

It's recently dawned on me that wall-warts don't have replaceable fuses,
or maybe they have no fuses at all.

No fuses at all with most of them.

That is not in the spirit of 13A plugs which all have fuses. Granted
they're to stop the wire burning up,

There clearly is no mains cable with a wall wart.

but it doesn't surprise me that some wall-warts burn.

The well designed ones don’t.

It would be prudent not to have them powered up when unattended.

But too much farting around to turn everything powered
by wall warts off when you can't attend them.