Because that is not against the rules right now.
There are dozens of government agency working on health problems , the CDC by itself has international impact.
So to make the government solely the responsible party for vaccine development is only to shut down those companies that already do better than the government does.
If the government can develop a vaccine or two , excellent, let them start already.
But the government is not going to outcompete private interests that have a profit motive .
There are certain things in which a profit motive is odious , in such matters the government is the proper responsible party. I don't expect contract soldiers or sailors to really replace patriotic ones for example.
But where development of something new is the point of the exercise , the lack of profit motive is crippling to government efforts.
Lets look at one of the great successes of NASA, landings on the Moon. This was a profit free great success.
But the Moon remains unexploited five decades later.
Do we want the science of medicine to proceed from useless success to useless success?
The science of aviation was greatly pioneered in the USA and the Wright Brothers sold a few aircraft to the Army. The total escape from orthodoxy that flying provided made the invention useless to the thoroughly orthodox peacetime military.
So aviation languished until sportsmen and other militaries developed it more, at the time that the US entered the fight in WWI we didn't have a suitable plane in production everyone had outrun our government dependent aircraft development.
Most of the vaccines make most of their money in the US , they are also mostly developed in the US.
What the government has been doing about this is to demand ten times the testing that they used to require , "improved " patent protections a bit too much, and mandated vaccinations regardless of cost.
We really don't need the government to take over , rather we need more companies involved and a real competition between them.