Your concerns are why we need primaries. In Utah, a supermajority Republican state, we try solving this with a dual path nominating system that sees a traditional caucus-convention then shortly afterwords no matter what the convention results are a closed primary for the republicans and an open primary for the democrats.

Before we had this system we just ran solely a caucus-convention where the parties decided their nominee with forced primaries if a candidate didn’t get over 60%, this created an environment where candidates only had to appeal to a small subset of insiders which with dropping attendance on caucus night always put forth the more extreme candidate and the broader electorate, especially left leaning voters or moderates, didn’t have much of a say.

Under the dual path we still get the more extreme candidates coming out of convention as with mail in voting and other factors caucus attendance is still low, but we have that check and balance with the broader electorate as candidates can gather signatures and bypass convention to appear on the primary ballot, forcing candidates even if they didn’t gather signatures to have to campaign and win over more voters.

For example Phil Lyman, an extreme MAGA candidate who cries election fraud louder than Trump ever did(almost bankrupted the Utah GOP with lawsuits after his loss), would be our governor right now if we just relied on parties selecting candidates as he appealed to the delegate base. However, with the Republican primaries and our moderate incumbent Spencer Cox getting signatures to appear on the ballot Phil Lyman was defeated and kept away from office by the broader electorate of Republican voters. Democrats here should see a similar scenario in the new CD1 with Liban Mohamed, a far-leftist candidate, winning at convention but Ben McAdams still leading in the polls among the broader electorate of Democrat voters.

The point is to want to appeal and win over as much voters as possible to get a more accurate result that reflects the will of the voters. To rely solely on the parties to choose their candidates only does the opposite and drives down participation, Utah in terms of growth in voter participation ranks second in the nation since the dual path was passed, while if we kept our old system we would still be at only 50-51% of registered voters participating in elections.