How basic are we talking? I mean, if your “basic” care covers, say, cancer treatment, it’s still going to be incredibly expensive.
On the other hand, I can see an argument to be made for some things. Prenatal vitamins, for example, cost little and can prevent the birth of children with mental defects that will leave them as a cost to the state for the rest of their lives. And anything cheap that can keep people from racking up emergency room bills that they won’t be able to pay (and thus pass on to everyone else) - such as antibiotics and whatnot - I can support that. Vaccines, too - you don’t want disease spreading.
But you have to be careful because people are going to try to pack as much into “basic” healthcare as they can. You know, where there’s a solid economic case that it saves us money to pay for something... good, go for it. But if the healthcare is to make other peoples’ lives longer/better, at our expense... it’s their responsibility to make their lives better. Anything else is socialism.