A few reasons:
- Don't have to burn a flame indoors
- It's a lot safer. I boiled large whole potatoes for over 30 minutes and was able to grab the pot handles with my hands and drain the water without using oven mitts
- You don't have to deal with a "hot ring" in your cookware when cooking, even with good/great cookware. Every gas stove I tried had this problem and this is the one that annoyed me the most. Induction heats the entire bottom surface area of the cookware, so you don't have to stand there stirring all the time.
- Excellent heat control. If you find a setting on a burner that works with a specific piece of cookware and a specific type of food - you can repeat it easily. As an example: I don't like my eggs crispy. I use a specific pan on a specific burner with the setting on my induction stove set to 6.0. This cooks the eggs the way I like them - every single time - there's no variation.
Now they do take some getting used to. It took me a month to figure out how to use my induction cooktop, but now that I'm used to it I could never go back to regular electric or gas. It's just too convenient.
About the only advantage of gas that I can think of is that it still works when the power goes out. That doesn't matter to me though as I have an induction hotplate and a generator. :o)
When you turn it on, it's hot right now, and you don't have to move the food off of the burner to stop cooking; just turn the burner off.
It sounds like you haven't used a real induction cooktop, as they all behave this way. Changes to heat settings are instantaneous, and if I turn off an induction hob that has a pot of boiling water on it - the boiling stops immediately.
Not all glass stop stovetops are induction.