There is one variety of flywheel that evades this problem. The magnetically confined kinetic energy storage ring levitates and confines a rotating ring via magnetic forces. The mass of the magnets and tunnel required scales in proportion to the radius, while the energy stored scales as the square of the radius. This does not violate the virial theorem, since the design is taking advantage of the underlying bedrock to carry the confining load.

It's a rather whacky idea, and as far as I know it hasn't been looked at for decades, but it is out there.

https://digital.library.unt.edu/ark:/67531/metadc173309/