And that is the most unlikely of outcomes. While it is not impossible, the probability of it happening are so minute as to be laughable.
Supposing the government was to finance 'genetic welfare?' Why would that be different from all the other times the government has stepped in to ensure the public health (which is an actual function of the government and why it exists)? Smallpox wasn't eliminated by private interests. And in fact, it's when those private interests become involved that things tend to get messy fast. Whenever you see instances of government inefficiency here in the United States, there's a good bet that there is a private company or business interest somewhere that's lining the pockets of whichever Congressperson is creating the mess.
In terms of genetic welfare, however, it is in a nation's interest to have healthy citizens, and that's not for some Orwellian concept of 'caste society.' Healthy citizens create a significantly lighter drain on health and other resources, while at the same time being more active in the PRIVATE (there you go) business sector that would ideally drive the national living standard up with productive work. Further, you've created a society where families are able to pool more of their resources towards other investments than health care, whether it be better education and living standards for themselves or just spending cash and driving a consumer economy.
It is in any country's fundamental self-interest to take charge of health issues where it can, because that is what ensures a country's continued prosperity and safety. Take this current measles epidemic, for instance (and no mistake: it's an epidemic). Because we live in an age where a person's belief can trump scientific facts and a library of documentation versus one discredited and flawed study, parents are refusing to vaccinate their children, and now we are faced with a situation where we have a measles outbreak that is significantly more severe than if there had been more studious vaccination.
That's not an issue of personal rights anymore: that's public health and welfare. If a parent refuses to vaccinate their child, they are not only putting their child at risk, but the health of every child around them. If you are putting people beyond your family at risk, you have forfeited you rights, plain and simple. There is simply a point when, whether you like it or not, the government is required to step in and say, "This is what's happening, and that is that. It is the law of the land."