Democracy doesn't work even when people get an opportunity to vote (unless the vote is 2-options, one round): See https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...
But it works even worse if voters don't get to vote. True.
But it works even worse if voters don't get to vote. True.
(For an explanation of what that means, see : https://politics.stackexchange.com/a/14245 )
Edit: though, if I had to recommend one, I'd probably either recommend "ranked pairs" or something exotic with a substantial deal of randomness.
Or, really, maybe I'd advocate that the primaries use ranked pairs, and that the general use FPTP (or something very similar) because it is easier to understand the mechanism, so easier for people to trust it / keep results seen as legitimate, and because parties narrow down the options to 2 for the most part anyway, and all the usual systems are the same once it gets down to two candidates (in random ballot voting, it is still different though)