Could we have though? Last I checked neither majir party has seriously persued this. So how are the american people to vote for it?
Yes. If you are genuinely unaware and not just asking a rhetorical question, yes socialized medicine is a major goal of the progressive left. We came close in 2010 but the votes in congress weren't quite there. The only reason major parties don't pursue it is because progressivism doesn't have the votes. You can definitely vote for it though especially if you participate in primaries.
So is democracy not real? I find it funny that when things do right it's because of our superior system of people choosing their leaders, and when things go wrong it's because people don't have any choice.
Democracy is a spectrum and the US system is but one poor flawed example.
Despite the founders being anti-party politics and wanting a spectrum of representatives each representing a block of the broader population and hammering out consensual deals that most can live with, the US has devolved into a two party system in which neither party especially represents 50% of the population despite both butting up against the median of actual voters.
This is the doom spiral of iterative FPTP and Hotelling's 'law'.
Other democracies have many parties, larger parties mixed with smaller parties, greater voter engagement, various forms of proportional voting systems (there are several), etc.
US democracy is just one example of many global democracies.