2kw per element is plenty of power, though you could definitely find more powerful ones. In my 3 years of owning an induction cooktop, I don't think I've ever had more than 1 element at full power at one time, it's really only useful for bringing water to boil, waaaaaaaay to much heat for anything else.
I'm not even sure if my entire house has a breaker for more than 32A.
Yeah, indeed, this is not esoteric physics. If you have a 10 kW electric induction stove (you can see the rating from the specs) and you want to operate purely on solar panels, you need at least 10 kW of solar panels and inverter etc.
Also maybe you want to use the oven and AC and charge the car at the same time etc. As far as I understand, it's a plus and minus calculation. It's not any kind of compatibility issue...
Naturally big electric power sinks need bigger voltages, otherwise the current and thus the cabling would get very thick.
If you want to run it just on solar, use one that can be legally fed with DC (almost all work fine, anyways), and hook a battery with suitable voltage between it and the solar panels.
If you are running the burners flat out. Which you only do when getting water to boil or preheating cookware. Once up to temp, induction requires far less energy to cook with since it is way more efficient - directly heating the pan.
So yeah, if you are in the habit of routinely maintaining four pots of water at a furiously rolling boil you probably will have problems. The rest of us are likely to be pretty safe.
The first one I looked the specs up on at my home center has a 4.8kW largest element and 8.6kW total. https://images.thdstatic.com/catalog/pdfImages/d9/d92c8678-a...