Yes if you support 40,000 units and your demand is much higher you're going to have problems. That tells you the system is underfunded. Central planning hasn't universally failed in every aspect and every application. Central planning tends to do poorly at solving problems that market mechanisms solve effectively, but it's sometimes useful at solving problems that market mechanisms solve poorly.
Centrally planned universal healthcare is generally effective and much cheaper than other systems. The US has out of control healthcare costs with its free market system. The next most expensive country to the US has less than 50% of the administration costs so the free market has actually come up with a bureaucracy that is more expensive to administer than what the government creates.
In general, central planning fails when market mechanisms are replaced by using force to allocate something. That doesn't mean opt-in programs with voluntary registration are going to experience the same type of failure. We know replacing salaries with a gun and telling people what they have to work on is a bad idea. That doesn't mean all central planning ever is a bad idea. I don't think anyone seriously argues we should abolish federal, state, city governments and let my local neighborhood manage it's own policy but that's the logical extreme of all central planning failing.