Have you done that math? The "even if 100% efficient" doesn't sound right to me. Wouldn't that imply gas cooking is 25% efficient?
Admittedly, induction isn't 100% efficient, but it's very efficient! A gas flame heats up everything around it, whereas induction only heats up your cookware. The surface of an induction stove without any cookware is cool to the touch; in other cases, it's warm only due to the heat radiated back from your cookware.
Induction also heats up the power electronics inside the cooker. That's why they need a beefy cooling fan.
I have done the math... Induction is 84% efficient, and gas is 40% efficient. So for most people, gas is still cheaper, unless you live in an area with very cheap hydroelectric.
Gas is 40% efficient at heating food? Where are you getting these numbers? I have no counter information here, but that just doesn't seem intuitively correct at all. With gas, you're creating a fire that is heating up everything around it!
Note that the 84% number is for a prototype model... 77% is for an on-the-market model, and it is beaten in efficiency by conventional electric for cookware matched in size to the heating ring.
Also, while gas is 'just a flame', the heat mostly rises, and right above it is the pan. Noticing that the pan, the hob, and the room feel warm/hot afterwards can be deceptive because the specific heat capacity of metal is 8x lower than that of the water in the food you're cooking, so you'd likely underestimate the efficiency.
Admittedly, induction isn't 100% efficient, but it's very efficient! A gas flame heats up everything around it, whereas induction only heats up your cookware. The surface of an induction stove without any cookware is cool to the touch; in other cases, it's warm only due to the heat radiated back from your cookware.