When a GOP official (or an official of any other party) says conventions pick nominees -- not primaries, they are correct. And that's the way our nation -- a republic -- was deliberately designed to work. It is not an "image problem" for anyone who understands the way a republic works.
Definition of republic: "A form of government in which power is explicitly vested in the people, who in turn exercise their power through elected representatives."
In Utah, we begin by forming a mini-republic in our neighborhoods where, on caucus night, we make rules for the operation of our precinct meeting, then elect leaders and representatives (delegates).
A few weeks later, those delegates meet with delegates from other precincts in another mini-republic (county convention) where they make rules for the party in that county and elect county-level party officers as well as nominees for local public office.
Others of those delegates elected at the precinct level meet with other neighborhood-elected delegates in a state convention (another mini-republic). Delegates at the state convention make rules for the operation of the party at the state level and nominate candidates for multi-county, state, and national public office. They also elect representatives from among themselves to be delegates to the national party convention. The process then repeats itself at a national convention.
The result is a party "establishment" at all levels that got where it is by common people getting elected as precinct delegates by neighborhood elections. Ultimately, a few of them get elected to top-level positions in their political party.
Bottom line: If you don't like where the nation or your political party are taking you, show up for your local political meetings. Get to know the people who want to represent you. Run as a delegate yourself. The only people who have a voice are those who show up when it's time to take a vote. If you don't show up, you have no voice. If you see corruption in the "establishment", show up on caucus night and election day to help start the cleanup.
And that is probably the root of Donald Trump's complaints about the Republican "establishment". Few of his fans have likely ever been involved in local politics. They don't know how a republic works from the grassroots level to the top. They don't know that the "establishment" consists of their own neighbors who simply took an interest and the responsibility in making the political system work to the advantage of their neighbors and themselves.
If, like Trump, you don't know the rules of the game, it's really convenient to say that the game is rigged every time the game doesn't go your way or to blame it on an "image problem".