I have had an induction cooktop for several years...like a lot of things, there is good and bad. The top stays cleaner easier than most other glass top stoves. It does heat up fast, faster than gas. Heat up speed does depend on how much mass you are trying to heat up of course. In example, if you have a small pot with 2 cups of water to boil you will see bubbles start to form on the bottom of the pot literally in seconds...put a half gallon on there and now it's comparable to gas.
I don't agree with the safety factor...any stove top should not be touched because if you don't know it's already hot they can all burn you. As to warping cast iron...no, not happening. Ferrous metal is how it works.
One thing I didn't take into account when I bought mine is that you now have to probably have all new pots and pans to cook with...they must be induction type or steel/castiron or nothing happens. This proved to cost more than the oven at the end of the day!!!
Bottom line for me...it's neat and it was new at the time, but honestly I probably would not redo the kitchen and include induction. Would there be things I might miss about it??? Yeah, but not enough to travel that road again.
Edit: Doesn't bother me now, I'm 54 and in excellent health, but the bigger pots and pans are rather heavy. Even aluminum ones because of the iron insert they need to work get pretty heavy. I could see this being some trouble for someone not in the best of health having to lift on "heavier than really necessary to cook with" pots and pans.