I've seen it claimed elsewhere, and have no reason to doubt it, that hard acceleration is in fact not more energy-hungry than mild acceleration. You just get to your target speed faster -- you're consuming more power, but for a shorter time, so energy can be a wash. Of course speeding up and then slowing down and then speeding up again is the enemy of economy, and since that kind of thing is often associated with hard acceleration, it can be hard to tease them apart.
Same said to be true of ICE, broadly speaking. Caveat, all hearsay and no I don't have a reference, but it sounds plausible to me.
Energy = power x time, but it's also force x distance.
So maximizing efficiency is about efficient force generation, but balanced by time-based overheads.
ICEV efficiency depends on keeping the engine revs in a sweet spot, being in top gear, and, for traditional automatics, locking the torque converter so the transmission is operating efficiently. That combination is why brisk acceleration from a stop is more efficient in an ICEV than slow acceleration.
EVs have fixed gearing, and generally the motors will be more efficient at lower rpms, so slower acceleration will be better for the drivetrain efficiency.
But drivetrain efficiency isn't everything. More power is better, as long as the "time-saving power" (extra energy used/time-saved) is less than other power overhead, such as climate control.