No. Taking off is a limit situation which is bridged by the clutch or torque converter. Once the clutch or torque converter are fully engaged it is all about power. If you keep talking about torque then you are severely fooling yourself. Look at the formulas and imagine an engine with a constant power output (my previous car had a flat spot in the rpm/power curve where the torque becomes lower with increasing RPM). I can prove mathematically that the accelleration is faster when staying in the maximum power output range rather than switching gears to get back into the maximum torque area.
Well, duh. Of course it is faster if an engine produces a fixed 100 hp.
But the reality is for the *vast majority* of internal combustion engine cars, it is not possible to get fixed power output at any given vehicular speed because the gearbox will never be able to keep the engine there. The exception is a CVT gearbox, which can probably most closely replicate the performance of an EV with an ICE. CVTs are unusual, though Honda and Nissan do make some, and the Prius has an e-CVT planetary drive set which replicates the performance of a CVT but uses two electric motors instead of a belt and cone drive.
In most EVs, the torque available from near zero rpm is full, limited only by the traction control system and the gearbox. So, say from 2mph upwards, the car can output full torque.
At the point of maximum power (when RPM * Torque = Pmax) the torque begins to ramp off. Attached graph shows this behaviour. Depending on the EV this is somewhere between 30 and 50 mph. For the Model S RWD85 it is around 45 mph. I believe for the P100D it is a bit lower because the vehicle is limited to 1300A from the battery. The power then remains constant until the Vmax of the motor is reached, typically this is due to commutation limits or sometimes just software.
Compared to an ICE vehicle, you would need to be at an RPM of ~2500-3500rpm to obtain maximum torque. So if you want to gain maximum torque on launch, you need a system like launch control, which holds the clutch just at bite point for longer so the engine does not stall as the car launches. This is of course terrible for the longevity of the clutch packs and in many owners manuals the vehicle manufacturer recommends avoiding frequent launches. But, the option is there.
EVs have this same launch characteristic (minus the slightly lower power output typically) without risking shredding the clutch plates. BUT, ultimately, it does not matter. Until you hit the peak power rpm of an engine, you don't get that peak power. So the initial launch is always torque limited, and therefore most EVs will do better than most ICE vehicles on launch.
My GTE has a "psuedo-launch-control" system. Pressing both the brake and accelerator when stopped when in the sport-GTE mode will start the engine and run it for 30sec. The car will still launch with just the e-motor, then at sufficient speed clutch in the engine, around 2000rpm and combine the power output of the two systems. The net effect is that the total system power of the car (~220 hp) is approximately fixed until 100 mph. The electric motor applies an opposing power curve to compensate for the engine's varying power output across the rev range.
Ultimately, torque is what moves you. That is the force in F=ma. Power is a necessary expenditure because you are moving a heavy car up to some speed, with air resistance and friction.
I do ask ... how many EVs have you driven? I have driven probably about 10 models, and ALL of them launch better than any ICE vehicle I have driven.