Here in US, I noticed most electric stoves, in houses use either the spiral burners, or ceramic glass surface. In Europe, I notice many stoves use cast iron plates over the burners that are sealed to the top with silver rings. These don't seem as common here, in US, except for commercial stoves and sometimes seen on portable units for house use.

We have a two burner portable unit, and it has these solid burners, one larger and one a smaller. I noticed, that even if switched on for just a minute or two, they take long time to cool down.

We have stoves with ceramic glass surface and cast iron plate burners here in Israel. But most of the burners are gas and not electric owing to their high heating efficiency. You can't saute with most types of electric burners (I don't know what with induction burners), but you can with gas burners.

Actually, gas is the least efficient in cooking burners. The amount of heat they throw sideways is phenomenal. That heat thrown to the side does not contribute to cooking food, but to increase the room temperature of the kitchen. There are two main reason they are still installed : the price of gas is way less than what it would take to make them comparatively expensive to run and the convenience of their use (such as sauté like dor mentions or the very fast, almost instant, reaction time).

Don't get me wrong, I cook with gas at home and love it very much.

I absolutely hate those cast iron ones. They take forever to heat, and forever to cool down. If you switch on the wrong burner by mistake, it is very inconvenient.

The main advantage of gas for cooking is the sheer power available. With electric (of any form) you can not go above 3kW input power on a single plate (with induction it means more than 2.5kW in your food, the higher efficiency I know), but with gas you can easily have 15kW input power burner, so even with barely 40..50% efficiency it means 5..7kW in your food, so more than double compare to the induction.
Of course you have to pay the fuel for this, but for quick cooking it is not that much.
And for just heat maintenance of e.g. a pressure cooker (that is, what uses to take time), you use the smallest burner on its minimum for quite a large pot anyway (otherwise it goes too wild), so the efficiency gets higher (the large bottom is able to eat up nearly all heat from the small flame). But that would, indeed, be more economical on the induction.

So the reason for gas is convenience (there is significant difference), not fuel/energy cost (very little; the gas is way more expensive if you take the ratio, but the total energy cost is very low, compare to e.g. the food itself, so even big factor becomes tiny difference when it is from "near-zero" base)

Gas also allows a certain degree of control in heating compared to electric. With gas, you directly vary the size of the flame and the amount of heat going into the food. With electric, the burner simply cycles on and off. Changing the knob doesn’t change the amount of heat coming off the element, but rather the duration it is being heated. There are a lot of people that prefer gas for this reason.

Our cooker has an induction hob, and it heats up incredibly quickly, and then supplies the heat at a constant rate until switched off, then all heat goes off except for the residual heat in the pan itself.