@Builder,
The selection of the NOMINEE does not have to be democratic at all. Want to know why we make a big deal of the conventions on TV with all the celebrations? Because originally the national conventions were where all the party leaders from all the states got together to bargain and choose for the party's nominee. There were no state primaries, there were no state caucuses. Then some states held primary elections, party members only, to choose who the state would vote for on the first round of the balloting at the convention. By 1968, though, only 12 states had primaries. In all the other states, the party leaders went to the convention to bargain for the presidential nominee.
An American's right to vote is only for the vote in November. On Election Day in November your choice is either
A. Write your candidate's name in,
B. Vote for the nominee of one of the parties. How that party chose that nominee is the party's business. The voter gets to choose which party's nominee he/she wants, regardless of how the nominee was selected. That's what makes the vote democratic.