I think that is actually a pretty good idea; measles is a terrible disease and it would be a shame for a child to come down with it and infect other children because his parents could not afford to pay for vaccinations. There are a few things that it makes sense for the taxpayers to pay for, and I think vaccinations for deadly childhood diseases is one of them.
Yes, the government paying for measles vaccines would fall under General Welfare of the Constitution.
As opposed to the thousands that die of the flu in one year, and we have about zero for measles for 12 years. Infecting children. I as a boostered and immunized parent could unknowingly carry the disease home to my child. People either can or are insured to get the shots, the only problem is that those who don’t are overwhelmingly the rich families who don’t give it to their kids.