You definitely can do high heat cooking in a pot. Most of them are stainless steel or cast iron after all, the material doesn’t care.

Sure, but most of the time when you’re doing high-heat cooking you’re not using a lot of liquid so a pan with its shallow sides makes it easier to get a spatula or tongs in to move things around. The high sides are only useful when you want to heat a large volume of stuff. Typically that means you’re using a water-based liquid (even something like a tomato sauce is mostly water based), so the heat will be at most 100C.

I suspect the British version of “pan” including what I’d call a pot must be from after North American English and British English diverged. The etymology of pan says that it has referred to a shallow thing since even before ancient Greek:

This is supposed to be from Latin patina “shallow pan, dish, stew-pan,” from Greek patane “plate, dish,” from PIE *pet-ano-, from root *pete- “to spread.”

I guess the North American English dialects kept this meaning of a shallow thing, whereas British English focused on whether or not it goes on a burner (which apparently you call a hob).