The MK wire terminals are certainly well designed. The nuts with captive retaining clamp and washer have been used on MK plugs since at least the 1950s.
As you say, most other brands have the screw and hole method, and doubling over the wire is just about essential on the smaller size conductors.
The overheating problem seems to be from the fuse clips. The MK type (and other good brands) clamp the whole length of the fuse's end cap, whereas many of the cheap brands seem to have rather thin clips which only "spot grip" the caps in a couple of places.
If you run say 2 or 3kW heater for a half hour, you can often feel the right-hand side of the plug getting quite warm.
