Efficiency for high power applications. You're decoupling a direct kinetic link between the engine (belt/exhaust gas turbine) for an electric generation method of some kind (regenerative braking? bigger alternator?) to produce the additional necessary power to spin the turbo up.
Extra complexity for limited / no gain at high HP. Why?
It's fine for low pressure, high efficiency engines maybe. But it's not an enthusiast level solution by any means.
Why don't we instead work on superchargers with gearboxes or something for more low end variable grunt then?
No you're not. Basically they're just adding an electric drive component to the turbo so that they can adjust the spooling of the turbo separate from the pressure created by the engine. It shouldn't add much complexity or cost and won't require a lot of extra power (actually can be used to generate power as extra pressure can be bled off and stored instead of just released by a wastegate/blowoff valve; it could conceivably replace an alternator).
It allows you better control over spooling the turbo, namely at low speeds, and at higher speeds when the exhaust pressure is pushing the turbo you can use the electric setup to generate electricity.
At least electric turbos I believe are that way. Electric superchargers are a different story, but through the use of say regenerative braking, you should be able to net more efficiency by removing it as a drain on the engine. In that case it'd be all about efficiency (so it wouldn't go into a performance car) as I just don't see that being able to produce the power boost you'd want. I think it'd also take a well integrated system, probably with something like pneumatic or electronic valves to really make it worthwhile.