For a single mug microwaves are quicker in America. Potentially even for 2 mugs.
BUT in America kitchen appliances have a power limit (usually) of 1,500W. This is usually higher than a standard microwave (1,000W). And since an electric kettle in America is just a heat source in water, it's very efficient. So if you're regularly heating multiple mugs worth of water, or just boiling water for cooking often, an electric kettle is definitely better. They are also pretty cheap.
Now in Europe and the UK, electric kettles are faster since they can often be around 3,000W or higher. But that doesn't mean American kettles are useless. American kettles a way faster than heating water on the stove. And WAAAY faster than heating water on a gas stove.
I love my electric kettle. I can get 5 cups of boiling water in about five minutes (less for less water).
And while a microwave is likely faster, it also heats the container. For a quick, single mug, it's not an issue. Run that thing for five to heat a lot of water, and the container itself could be scorching hot.
It would burn your food. Microwaves heat the outermost layer that contains water. That heat conducts inwards. It's the same reason you don't bake everything at 500F.
They absolutely do. Many microwaves in the UK are about half the power of built in American microwaves. (Portable/countertop microwaves are extremely common, being around 700-800W usually)