Would cast iron pots and pans count as thick-bottomed in this case?
I usually use these with electric stoves since they retain heat pretty well. They take a while to warm up though, so there's both time and energy lost in that warming process.
The best vessel is a flat bottomed one with at-least quarter inch thick bottom.
Cast Iron ones will do too.
If you have to cook something to simmer and hold heat for long, best use thick bottomed ones.
What could be done to mitigate the slow heating issue is to use a small amount of water initially, on high settings, allowing it to boil. Then you can add your contents, reduce the power setting and allow it to simmer.
What many dont know is that you can keep a cast iron or steel plate between the vessel and the stove, of a suitable thickness, that converts the induction stove to a "heater" stove (the plate gets heated through induction, but the vessel only sees the heat). However, a word of caution. If the plate is of a very large size, it will have un-even heating and may warp. Best size is one that is slightly smaller than the circular marker on the stove.
I primarily use cast iron for cooking, and it does help with the hysteresis, but I still have a problem with the bottom of the pan being way too hot and tending to burn food.
I usually use these with electric stoves since they retain heat pretty well. They take a while to warm up though, so there's both time and energy lost in that warming process.