I remember reading somewhere that electric compressor stages are apparently getting used to reduce input lag on automotive turbo chargers.
Yup, E-Turbo [1].
[1] https://www.motortrend.com/how-to/e-turbo-electric-assist-tu...
Though borderline possible, it is very hard for solid fuel rockets to make it to orbit, and they have horrible payload to total mass ratios. It all has to do with the specific impulse of the fuels, no solid fuel provides as much as hydrogen/oxygen.