People explored them in the 2008-ish climate boomlet and it was hard to make the physics/costs work. If something has changed since then it might be worth looking at again, else that's probably why nobody is pursuing them today.
Physics work, but cost has historically been the issue. My current project involves driving down the cost to make extremely affordable 50 kWh flywheel modules.
Sized to fit in a car?
No, stationary only. It’s modular, so you can combine as many as you need for grid-scale storage.
A stationary car…I’d imagine it would make steering difficult. And if you had a crash…!!