so they have to routinely change the the tiny circuit breaker at the consumer unit,

If I understand the nomenclature correctly, your "consumer unit" is our "load panel" or "breaker box". We use 15A or 20A breakers for our typical outlets.

If you used unfused plugs, your lower-rated cords could potentially reach fire temperatures without drawing enough current to trip the breaker in the consumer unit. Which is why you use fused plugs: to protect the lower-rated wiring from higher current.

The US uses a different approach. If we used power cords rated to 5A for a 5A appliance, and we plugged them into a 20A circuit, we could have the same problem: A 15A fault current through this cord wouldn't trip the breaker, but could start a fire. So we don't do that. Even on our lowest current, corded appliances, we use a cord that is rated to carry a 20A fault current capable of tripping the breaker.

(You will occasionally find cords rated for 7A. This is 7A duty current, and the limitation is because of the specific appliance socket, which has a fuse immediately inside the casing, and other restrictions. The 7A rating is not on the wire itself. On these cords, the wiring is still required to have a fault current rating of 20A)