So your freezer shuts down when your toaster is on? A hard cap that's low enough to make a difference seems like a bad idea, there are many devices which shouldn't be cut off suddenly. And that's ignoring things like medical devices.

Of course there's already a hard cap (usually ~9kW over here), but I suspect most people never reach it.

There are plans in Belgium to charged based on peak power (something silly like "max power used in any 15 minute period"), which would drive up the cost for the average consumer without reducing demand (as people tend not to have much choice in when they use their most power hungry appliances).