I would even go to say that the reason Starlink exists is to use up SpaceX excessive launch capacity. With its idea of building assembly lines and reusable rockets, can launch more stuff than there is market for. So they create their own market. Starlink launches are almost free besides the fuel, as they have rockets lying around that are already paid for.

A state-funded competitor could come up though. China for instance may want their own satellite internet for strategic reasons, and fund that. I am sure Russia would be interested too. This in turn, will pay for development of a reusable rocket program.

Lets cool down a bit. Falcon 9 launches cost much more then 'just the fuel'. Estimated launch price is still 10-20 million $. The Upper stage is an expensive thing to build. Operations cost are also not that low. Fuel cost are only like a couple 100k$.

China is deftly building something. Russia doesn't have a snowball chance in hell of building something like Starlink.