Plugs are a subject in their own right
http://bs1363.fatallyflawed.org.uk/
13amps is interesting as well. They will get warm which some could describe as overheating. Going on experiences a bit of a long time ago the company I worked for made an EV charger that took a perfect 13amps from the supply. The idea was overnight top up charging. In practice 10hrs or more. Few plugs and sockets were up to it. Mk was a make that survived so have never ever fitted anything else since. Recently 3kw 220v maybe 240v space heaters are around. Even on modern MK the pug gets warm going on one I have. Some of that may be down to the max wire size that can be used in plugs and it not being an Mk plug but UK plugs have changed over time. Traditionally makers might limit max draw to 2.4kw knowing it's unlikely to cause problems.
One thing that struck me about the push down type connectors is that they imply plastic pressing on metal only when the connection is made.
While I like use of the cam types they could be plastic pressing on metal to make the contact. Self loosening if they get too hot. Never looked so don't know. To be honest I prefer conventional screw type methods of joining. About for donkeys years in enormous numbers and seldom cause problems if correctly tightened, even barrier strips but a pity they don't have a leaf in them as some types do intended for other uses.
I seem to remember the Hospital board had a red plug made for them with no fuse in it, I remember my father-in-law had one or two he had picked up in error, not sure if the fuse was in the equipment or not, but taking 13A over an extended time has always been a problem, and when the pins were made with a insulated collar they were less able to dissipate the heat.
For immersion heaters it was common to use 15A plug and socket with no fuse in the airing cupboard.
But the push in wiring connectors have been around for a long time, first I worked with was 1980 working for a Dutch company in Algeria, so a good 40 years, they were a huge improvement with panels as serving was basic put a screw driver in each terminal and test for tightness, over time it would neck off the wire where the screw had bit in a little more each time tightened, even torque screwdrivers did not help. The main problem was plant that could vibrate, the spring loaded terminals removed this problem, it did however mean every stranded wire needed a feral on them, however you needed a feral to hold on the marker anyway so that hardly mattered.
However I think this thread was more about domestic, and hard enough to get wires over sleeved with brown or blue, never mind a cable marker, and in a panel the majority of the wires were control and very little power went down them. If I had wired the machines I worked on like the normal house is wired I would soon have been kicked out, we called them house bashers and it was seen as the lowest part of the trade.
OK that is hardly valid today, things which were only found in industry have now arrived in the house, the most complex house wiring was the central heating, things have changed over the years.
I also was involved with EV chargers, we used Reyrolle plugs and sockets in early years
Later went to the type now found on nearly every caravan site, there was one where you turned the plug to switch it one, and pressed a button to switch off and release the plug.