The main reason you can't get rid of them is that it would require a totalitarian society. Say a bunch of people want to start a party. They decide that rather than just the inner circle picking who the representative will be, they want to involve all the party's supporters by having an election. The TS wants to make that illegal. How does he propose to stop it? You basically have to tear up the Constitution (no more right to free speech or free assembly, for example).
You're wrong about Clinton and Reagan, BTW. Salient issues change over time, and there's some drift, but both would be highly electable in primaries today. Clinton is still alive, and no one regards him that way. Reagan was a lunatic would would have changed with the times.