We drink an unbelievable amount of tea. Firing up the hob each time would be silly, when you can fill a kettle to the minimum and have boiling water in an incredibly short time. Not much more than half a minute with a good modern kettle.
It does in theory. There are a few taps in the UK that are marketed as being able to produce essentially boiling water (which is what our typical tea bags require). Though we tend not to put quite so much money into our kitchens.
And we would wear those things out, I swear! :-)
I think Americans think British people drink tea out of poshness, when it is the opposite. Most of us also like a posh tea now and then, some of us drink expensive leaf teas... but the majority of what we drink is optimised for fast brewing off boiling water: tea that goes black in the mug in thirty seconds in boiling water.
There is a concept here of "builders tea" -- the kind of thing a builder drinks -- which is sort of the functional equivalent of cheap electric coffee-pot coffee. That is, it's the kind you know isn't the best, but you will still drink it, and that cuts across all class lines. [0]
There is a parallel thing: the "tea urn", which is like an enormous samovar with a lever -- that you still will see in industrial canteens and at church coffee mornings and at gatherings that aren't at cafés or restaurants. Those things actually need a different kind of tea, which brews more slowly and at slightly lower temperatures. The end result is a bit like builders tea. But we wouldn't bother with them at home.
[0] We do absolutely drink coffee at home, but aside from appalling instant coffee we tend to skip over the coffee-pot coffee in the UK, to slightly more expensive ways of making coffee or to dreadful Nespresso machines. You'll see more of those or Bialetti mokas here; old style electric coffee pot percolators are now rather unusual. But Alan Adler's Aeropress particularly caught on here among coffee nerds, because that is really compatible with electric kettle life.
