the efficiency lost with the comversion of mechanical power to electrical then back cannot be worth it
Um, that's true of most shaft driven superchargers. Remember, the things were invented to enable airplanes to fly higher by maintaining sea level mass airflow at altitude, not to boost specific efficiency or gross power. It's true that if the VE on the engine is low, you can get some net gain from supercharging, but you've added weight, complexity, and heat management issues to your engine to do it. The math doesn't uniformly work out beneficial - if it did, everything would come with a shaft-driven supercharger. I suspect the major reason it's so popular on Lotus is that we have alloy engines and light platforms, so hurting the power/weight ratio of the powerplant for more gross output isn't all that horrible an idea if everything is sized just right.
The magic to an electric supercharger is that, like nitrous, it is extra power
just when you ask for it. Unlike nitrous, as long as you put it behind the MAF, you should get some goodness from it up to the limits of the ECU, injectors, and MAF to understand what you're doing without having to have a supplemental fuel injector. Running an electric supercharger all the time is indeed dumb. Running one when you're at WOT and going up through the gears should work out quite well as long as you have enough amp-hours in the battery to keep it going for the 10 seconds you need it, and you limit the power draw of the alternator during the recharge cycle. BorgWarner sells one as a fix for turbo lag, which is also one of
AerisTech's use cases.
Magic? no. Useful? Maybe. Depends on the use case.