But the downside is you'll need compatible cookware, which can be expensive.
I'd rather pick proper cookware (eventhough the initial investment will be much higher, the "running costs" will be lower).
But you might not have new pans, nor the money to replace all of them. Especially if you rent and have no control over what stove gets installed when your current one breaks - or just move into somewhere to discover the induction stove. It is kind of like buying toilet paper: It doesn't matter if the 24 pack is cheaper if you only have the money for the 4pack. Running costs don't always matter if you don't have money to invest upfront.
And to be fair, they aren't inserts. They sit between your stove and the cookware. The plate heats up and heats up your cookware, much like your pans heat up to cook your food. It might take slightly longer, but it won't realistically be worse than heating up a cast iron skillet. And you have a stovetop you can use.
https://www.bartscher.com/en/Kategorien/Kochen/Induktionskoc...
So the conundrum is... toss the pans I gave my wife over 20 years ago? Or just stick with electric burners.
If you like to cook (and I'm assuming you do, considering that you bought expensive cookware), I would definitely recommend auditioning an induction burner before you go through the expense and hassle of switching out your stove.
Higher quality ones usually scale more linearly with the power setting.
Most of the ones you are referring to are European models that work on 240V. If you know of one that works on 120V, please point me in that direction.