SpaceX provides a per-seat, per-launch cost, not a direct government subsidy - That would be ULA. ULA was literally a direct mechanism for transferring tax revenue to large multi-national defense companies to procure "independent access to space" (sound familiar?).
They do use (and pay for and lease) NASA and Air Force facilities - but in America, airports are government institutions as well, that are explicitly leased out to airlines. Reuse of NASA's unused resources, rather than destroying them (or paying for the upkeep) after the shuttle program, was an explicit political decision.
So why isn't SpaceX cheaper? They have kept prices high (but still lower than everyone else) to help fund Starlink. The fact that they can do so is reflective of Falcon's costs.
Reusability is real. Ariane 6 is nothing more then the ULAification of Arianespace.