Pushing the batteries and motors harder results in more waste heat. So the harder you accelerate, the less useful energy you get, i.e. lower range.

Your physics instinct is right in a vacuum.

Same speed should be the same kinetic energy.

But the real world adds losses, and those punish hard acceleration:

Electrical losses scale roughly with current², so flooring it wastes more as heat

Motor/inverter efficiency drops at very high power

Tires waste more energy under high torque (slip)

Drag starts biting earlier if you hit high speeds sooner (ever ride a bicycle?)

Moderate, steady acceleration is most efficient. Not crawling, not flooring it. Use ~30–60% pedal (middle way). Smooth, continuous push.

You can still have quick launches occasionally without wrecking your efficiency. Just don’t make it your default mode.

In electrical terms you’d be pulling more power from the batteries and over any cables, P=I^2R which would technically result in more losses in the conductor at higher currents. Also depends on the efficiency of the batteries and motor.

I can only speak anecdotally, but the anecdote comes from years of driving an ev. When I'm driving, the first ~8 miles I have to drive to get anywhere involves a long sequence of stop and go lights. I've experimented with both aggressive and very conservative acceleration in this, and what I've found, is that it really, really doesn't matter.

Its practically the same. My thinking is basically that energy = energy. As long as I'm not overshooting the target speed, the rate of acceleration isn't relevant. It takes the same amount of energy either way (in terms of observed, battery based kwh). Basically, if your target speed is the same, it doesn't matter if you are getting to that target speed faster or slower. It takes the same kwh to get the big lump of mass from rest to that speed.

Now where I do find efficiencies is in what that target speed is. Even a bit of traffic massively increases my battery efficiency.