If you have a 16A CEE Commando plug, you've probably got a 30A MCB behind it. As you say, a 1000W PSU probably only needs a few amps, so you'd want to use fairly spindly wires and a 6A MCB. However, if you have a 3kW spindle motor, you'd be wanting a 16A MCB and fatter wire.

The main difference between an MCB and a fuse is that the MCB can be reset easily - and can also be used as a switch. If you don't like MCBs, fuses are good but you should fit something. You don't see a 60W laptop PSU supplied with a 13A plug....

I've got a fair idea what I'm talking about when it comes to PSUs and VFDs, as designing them has been my job for the last 36+ years ;-)