> I think it is fair to say that through the nomination process, whoever is voted to run as the Republican nominee for president is considered to be the best representative for the party.

It is not fair to say that at all. The primary system is highly undemocratic, and what’s more, the people who participate in it aren’t statistically representative of Republican voters as a whole.

Even if you are voting against someone, the person who you voting for is the person you find the most palatable of the options presented. I also don't think you can look at the de-facto leader of the party and say "in some cases" as if the president isn't a big case.