The thing is that in a real free market, there wont be just 1 person inventing the cure, but many separate people, not even knowing of eachother. [which is highly inefficient because they are not communicating and sharing ideas. Actually, this is very similar to the hashing problem in BitCoin, where if all the miners cooperated, they could cover the hash space just once. ]

And they would compete about who can release the vaccine faster to earn more money. The person that invents it first, will quickly start to sell it before the other people invent it, to ensure that he profits the most. And when the other start to sell it, the price of it will drastically drop. [Unless they go into monopoly, keeping the price high.] So the vaccine will be on the market ASAP. Greed is a 2 edged sword, and in this case, greed will save many people's lives, because as greedy is the inventor, as fast the cure will start to save lives. So if 1 out of the 100 inventors withholds the cure, he will just lose money, as the other 99 people did the right thing, and will be rewarded with big bucks.

If you have 1 point of failure, a communist research department, you can just have 1 evil person withholding the cure because he believes the "people" are not ideologically pure enough to receive it, or some other disturbed ideological delusion, and will let people die.
[And the same could happen in the free-market, by someone not interested in profit.]

Doesnt matter what system you create, if you centralize power, you wont create a paradise, but rather a hell on earth. [I guess that your body is "hell on earth" then.]

A free market is just there to balance power, nothing more, nothing less.