The built-in cooktop in my Sprinter camper is a 1500 watt induction unit:
It works very well. No worries, of course, off of shorepower. It also runs fine off my ProSine 2.0 inverter/charger connected to a 300 AH AGM battery bank. The issue is, of course, that the rate of discharge from your battery bank to run a high-wattage appliance (be it cooktop, microwave, heater, A/C, etc.) is way over what's deemed desirable. My run time for the cooktop is usually 5-10 minutes at a time, so I am not running the battery bank too low, but I probably am shortening the life of the batteries by some significant, but not intolerable, amount.
I do have a portable gas cooktop that I carry for times when I'd need to do more than incidental cooking when away from AC power. My view is that the induction cooktop is brilliant if you'll largely have shorepower available, but that propane would be preferable for extensive boondocking unless you have a quite large battery bank.