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)
I think many concerned believe that making sure their party gets elected - no matter how - is allegiance to their country. It's internally consistent if you genuinely believe that the other party seeks to destroy your country, and therefore is to be opposed by all available means.
The reluctance to let people register to vote is understandable, if your allegiance is to your party before your country. I suppose they rationalise it by convincing themselves that what's best for the country is for their party to be elected, rather than a free and fair election. Or maybe they tell themselves "I'm sure the other side uses similar tactics". Or maybe they just don't care.