I think you are overstating the persistent political difficulties a single-payer system would encounter. There has certainly been vocal conservative opposition

I think you are overstating the persistent political difficulties a single-payer system would encounter. There has certainly been vocal conservative opposition to Social Security since its inception, but its beneficiaries form such a powerful lobby that it is effectively untouchable. I suspect that once enacted a single-payer system would be so popular among its beneficiaries (i.e. almost everyone) as to be unassailable. Something similar is happening right now with the ACA.