I respectfully disagree. Full-on capitalism of the scale necessary to manage technological problems the size of even local space exploration is not known for its ability to do things safely and repeatably without failing. This is due to an excessive focus on profit and cost control. Because of pressures in those directions, and management failures of the type where management overrides the concerns of engineers and scientists, people have died in catastrophic circumstances three times during the American space program. (I am not including numerous deaths during flight training.)
The NASA program has not been a purely "government" program like the Soviet space program was; there has been constant and ongoing participation by civilian entities, whose
The crew of the Apollo 1 spacecraft died in their incomplete spacecraft during a training session, when their pure-oxygen environment was triggered to flash-fire by an electrical fault that sparked. The pure-oxygen environment was heavily debated but was pushed through because of cost factors. The crew objected strenuously to the excessive amount of flammable material that was present in the capsule (in part because the technical crew working the simulator was unable to keep up with the obnoxiously high rate of change orders.)
This is symptomatic of a program being pushed out before ready for political reasons, which is an identical process (and generally, more severe) in a profit-driven organization which has to deliver on a schedule.
The Challenger crew died because management overrode technical concerns about the thermal expansion qualities of an O-Ring that was chosen for primarily cost-driven reasons. The civilian corporation that provided that O-Ring had given specific temperature ranges, and their engineers were concerned about the use NASA was making, but was overridden by their management. When their concerns were pushed to NASA, the management there, concerned about the impact to their program of yet further delays when dealing with an anti-Space movement in Congress, ignored the warning.Note that this was not the first time the O-Rings failed, and the management had "normalized" this unsafe deviance from the required performance.
As you know, the presence and persistence of safety and health regulations and their investigators is considered an unnecessary negative cost by most corporations, who constantly lobby to have OSHA funding restricted (and quite successfully, as well.)
The Columbia crew died because management had downplayed the danger to the craft from the flying debris that damaged the insulation over the left wing, resulting in thermal damage to the wing during re-entry.
The debris was an unusually large piece of foam (hardened foamed plastic weighing several pounds, and was seen in the recordings of the launch, so they knew it had happened and there was some concern about whether it was NASA rejected the opportunity to have the DOD cameras image the wing (three times) even though the DOD specifically asked to do so; they had the capability, obviously. The reason they did so was, according to records, based on a spreadsheet tool that measured damage risk from ice impacts. NO testing had been done to validate the damage from foam impacts. Ice impact models predicted approximately what was shown to have happened.
In a group-think failure, both management and engineering managed to conclude that their tool wasn't accurate for foam, so there was no risk so no imaging was needed.As with the O-Ring failure, the fact of repeated foam strikes having NOT caused problems, caused this deviation from standard safety considerations to be 'normalized' - situation normal, why worry?
The disregard for the risk of wing damage also meant that they did not take a space walk to see whether the thing needed fixing.
So, in conclusion: the combination of governmental and civilian agencies, operating under capitalist principles, did not prevent catastrophic failure. Capitalism alone uses cost-accounting to determine whether the lives lost are "worth the expense" when the final profits are considered. Ergo, there is no reason to think that capitalism would be in any reasonable way superior to what we've had.
What the Falcon 9/Dragon launch proves is not that capitalism is innately better - considering they had the advantage of all the previous space science, which was definitely government-sponsored - but rather, that NASA and our government have become so very very conservative (and so dominated by anti-science, anti-Space, and anti-innovation thinking) that they have lost sight of the very real benefits of going into space. And as a government agency it has always been considered beneficial to control access to space, which is where the real problem lies.