That and because UK uses a ring circuit, which was seen as a solve for a copper shortage at the time.

Ring circuits generally way higher in power - and a lot more than a single appliance needs or could handle. Hence the need for a fused plug.

The upside is each socket can take a 13A plug (circa 3kW), whereas a standard US socket maxes out closer to 1.8kW.

Maybe true, but BS 1363 dates to the late 40s and the Schuko illustration below is from the early 30s:

https://en.wikipedia.org/wiki/File:SCHUKO-Patent.svg

Rather, I think the British decided to iterate (for better and for worse) on their earlier design that looks a lot like BS 1363.

Personally, having lived for an extensive amount of time in places with Schuko ("Europe"), NEMA ("US"), and BS 1363 ("British") plugs/sockets, I will take Schuko any day over the other two. Schuko stays in place, is grounded when it needs to be, is flexible when it comes to how it leads the cord out of the plug/socket, and so on. For all the touting of safety, "no sparks", etc. that we hear about BS 1363, I have never seen it out of a Schuko (NEMAs on the other hand...). Yes, BS 1363 improves upon NEMA, but that is a very low bar.