In fairness, and NHS didn't get tested at the ballot in 2016. There's a structural problem with parties of the "left", namely that they're hostages of their predominantly centre-right memberships. Labour in the UK has the same problem, as do the Socialist party in France. Pretty much all social democratic parties have been hollowed out by a managerial class (alongside career lawyers and the like) that their traditional bases aren't welcome. This stymies the ability of left wing populists who would challenge the current system and bring about policies like universal healthcare to even run in the first place.
What's worse is that they'll inevitably be attacked by those same centrist incumbents while they do run: Jeremy Corbyn was a great example of this. One of his fiercest critics is now a minister for health, another was made a Lord, others are now safely pickled in think tanks which will tide them over nicely until they can return to the fold.
The only way to fix this is to do as the right have done across Europe: to accept that it'll be a very long haul indeed until your people get power, and to start insurgent, radical parties. This sidesteps the big incumbent parties as a filter, and makes it clear who one's friends are. That's what needs to happen in the US on the left, but the odds of it paying off in anything less than decades are staggeringly low.