I use a single area induction hob, it has a maximum power of 2 kW on switch on defaults to 1 kW and I find even that is too much, for most cooking between 400W and 600W. What you need to remember all the heat goes into the pan, so it needs less heat than a standard hob.
In my own house we have a stand alone cooker with 4 heating areas, on boost I can put 3.6 kW into one pan, however the only time you can use that much heat is to boil water, add anything to the water and it just burns with that much heat. So without boost limited to 1.8 kW and other than when we first got it and I wanted to play, never use boost.
My daughter has a 5.5 kW gas ring, I saw her boil the water in the electric kettle then poor it in the pan, my question was why? She did a demo filled the kettle to spot on the mark and poured it into a pan, then filled the kettle again to spot on the mark, she lit gas then switched on kettle, the kettle won by a huge margin I suspect most the heat from gas goes into the room not the pan. But of course when I got home I repeated the experiment with my induction hob, select a heat area of 3 kW on boost, and filled the 2.8 kW kettle. Result near enough the same time, since kettle is only 2.8 kW and ring was 3 kW suppose kettle did have the edge, but only just.
So at around 700W average per ring from experience that is ample, it would not be with any other type of hob, but it is with induction. The only down side is the silly touch controls, I fitted an induction hob for mother with touch controls, and had to replace it, at the angle of view in a wheel chair she could not see the touch controls, also with my hob at home when it starts to boil a quick turn of knob and power is off or reduced before anything boils over, with hers however you had to first select the heat area then touch multi times to reduce heat, by which time it has boiled over.
The cheap Lidi single hob I use at mothers has a knob, but it's more like the wheel of a computer mouse you can spin it round and round and it does not switch off the hob, it just goes to minimum of 200W, however the touch control to switch it on and off, only needs one touch to turn off, so with that hob the touch control works OK. So if you have touch controls, make sure it will switch off with a single touch.
I will admit I like knobs, anti-clockwise against stop and then to simmer setting and it auto boils then simmers, clockwise against stop and it goes to boost, both outside knobs right clockwise left anticlockwise child lock on or off, easy to glance down to see settings 1 - 12, from melting chocolate to 1.6 kW the knobs give all the control you could want, why they use touch controls I don't know, but there are very few with knobs on.
It was a pain getting new pans, we got caught out with stainless steel pressure cooker, stainless steel does not work, it's not magnetic. However we now use a stand alone pressure cooker, much better, you don't need to watch the pressure all automatic. Not sure of safety of pressure cooker on an induction hob, at 3.6 kW that's a lot of heat, not sure the pressure relief is really man enough for that much steam? We also have a plastic pressure cooker designed to go inside microwave!