Wonder how long it would take to recoup the $6K cost of the stove?
I believe it will never happen.
For starters, you would only need to recoup the difference between the $6000 price of this item and the price of whatever else you consider buying. Unless your other option is a professional grade unit, such as a $8000+ Viking unit, you are likely to find a very acceptable unit under $2000. So then, how long will it take to recoup the additional $4000? At 16 cents per kwh (a representative, average number in Illinois), you would need to save 25,000 kwh.
Here's the essence of the situation: the amount of energy (in units of kwh) it takes to boil a pot of water is the same, no matter what energy source you are using (i.e., gas versus electric, but let's stick with electric for now) or the method used to cause the pot to get hot (i.e., electric coils versus induction). It's all about the amount of energy absorbed by the water, water that is unaware of where the heat comes from. The difference boils (pun intended, with no apologies) down to the efficiency with which the source converts electrical current to heat.
Induction heating is more efficient than electrical coil heating, but by how much? Suppose it is 50% more efficient (I think that is way too generous). So if coils will use 25,000 kwh to do their job over some period of time, induction can do the same job for only 12,500 kwh. Looking back at post #8, and not considering all burners running at maximum, let's say you are using 1kw on average, while using on an induction cooktop. If you use the cooktop for 4 hours a day (that too is a bit generous), equating to 4 kwh a day, it would take you over 3,125 days (just over 8 years) to save a total of 12,500 kwh.
Realistically, I would estimate the time to recoup the extra $4000 to be more like 15 years. And if your chosen unit cost under $1500, the recoup time would be much longer.