I would not say caramelized, but I certainly get significant browning in less than 3 minutes in a wok on a 7 500 W work burner.
Most ordinary stoves are about 2 000 W, but apparently professional stoves go to 4 000 W, and the professional “jet engine” work burners in many restaurants achieve 20 000 W.
On the flip side, to your point, the large burner on my stove is fine for a wok (I'd have to look up the output) but it's a lot more than a typical electric stove would put out (and hears up the sides)--which is why America's Test Kitchen recommends people use a skillet rather than a wok.
And “professional kitchens” often have everything at temperature already - the wok was just used moments before so there’s no preheating.