Took the words right out of my mouth. If the Republican party did disappear (I don't think Trump could actually do this, but let's suppose) another party would appear, and frankly it's hard to imagine how it could be worse than the Republicans.
Ultimately the electoral system determines the party system, and an FPP system like the USA's is always going to produce two large parties.
Although, in a partial defense of one-party states, while they are not ideal, they are not necessarily as horrible as the term implies. Japan and Sweden were both effectively single-party states for decades (although in both cases the system broke down) and I wouldn't say their political systems were any worse then America's two-party system.
TL

R, any democracy that relies on the existence of the G.O.P. to be viable is a pretty shoddy democracy