People know best how to spend their money. The government shouldn't effectively force people to consume healthcare.
Especially when there's evidence out there that programs like Medicaid provide no net healthcare benefit to recipients. Health outcomes might even improve, if the money that would be going to Medicaid instead goes to people spending more time on self improvement and health.
ETA: That said, feasibility is always the question. Given that, I'd be happy as a duck to make the basic income only $8,000 a year or whatever. Then again, I'm one of the austere basic income advocates--I'm on the fence about the Swiss proposal because I think it's far, far too generous, even considering the higher COL there.
Private health insurance is much more expensive per-capita than Medicare and Medicaid and you would have to increase people's basic income to be able to afford it. Except that wouldn't work for people with preexisting conditions--they would be left to die in the streets. You'd have to regulate health insurance companies to accept everyone, but then no one would buy health insurance until they were already sick, at which point everyone has to buy health insurance, at which point you might as well implement the Canadian system because that's already less costly, per capita, to the federal government alone, than Medicare and Medicaid are.