Does a "take-off" assist make sense for electric aircraft?
Yes it would, for fuel based aircraft and for electrical ones. The higher the MTOW, the larger the benefit.
This article makes a case for installing catapults on runways for commercial aircraft: the engines are dimensioned for the take-off, and an assisted takeoff means lighter engines with the associated fuel burn savings. Take-off is particularly demanding on the power installation because it needs to acquire a lifting velocity from standstill.
Other power-hungry flight stages:

TOGA for go-arounds is applied when the aircraft is at approach speed. The more the better of course - but why should GA power be max TO power for the highest payload ever, on the hottest day ever, on the shortest runway ever. This is what the engines are dimensioned for. From the wikipedia article:

..the engines then increase to their computed take off power. Modern aircraft flight management computers will determine the power needed by the engines to take off, based on a number of factors such as runway length, wind speed, temperature, and most importantly the weight of the aircraft.


Climb power is set after TO: a lower thrust/power setting is selected after the TO. When reaching cruise altitude the thrust/power setting is reduced further. So the engines would be dimensioned for the climb stage.

Aeroplanes certified under 14CFR part 25 must be able to climb after a single engine failure after $V_1$: twin engined aircraft will be dimensioned for this case, if the launching device accelerates the aircraft to a high velocity such as $V_4$ there will still be an engine size saving.
A steam catapult will do the trick, or any of the options that OP states. Of course, the take-off run should not be the couple of metres that an aircraft carrier allows, but should be longer to limit the accelerations that the structure is subjected to.