I don't know how effective this was. Did it backfire by promoting economies of scale in a program that went on to sell to adversaries anyway? Did it murder the domestic engine programs and did that have knock-on consequences? I don't know if the policy was effective, but I do know that stopping "engine proliferation" was a widely given and accepted reason for those programs.
Of course that means not leaving them over to the bear.
I mean, for many years the US bought seats on Soyuz launches, so that was an even more direct mechanism.
Another way to look at the price is from supply/demand angle. Even if real cost of falcon 9 launch is much lower than its price, SpaceX can not just lower the price, otherwise they will need to handle even greater demand.
Even with current price their launch cadence grows exponentially year by year. With lower prices they would need to grow even faster.
If you don't gain any additional volume by lowering cost, it doesn't make any sense to lower your cost.
It also doesn't help that Rockets (for fairly obvious reasons) are highly regulated, which further distorts this market.
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.