Early on in the book, the engineer running the Comet stopped for hours at a broken signal and spent hours waiting for someone to tell him what to do.
However, later we see that almost every engineer working for Taggart Transcontinental volunteered for the first run of the John Galt Line (and that numerous other staff members volunteered for other positions as well). The only exception were 3 who were incapable of doing so for various reasons (e.g. the fact that one of them was in jail for reckless driving).
I suppose that it's possible that the aforementioned engineer of the Comet was either one of the three or had left the company by then, but there's a good chance that he was one of the people to volunteer. Even if he wasn't, odds are there were plenty of people like him who volunteered.
That being the case, Dagney decided who got to drive it by randomly drawing a name. There's no indication that either her or Eddie had done anything to screen out the obviously bad engineers. She drew one of the best engineers on the line, but that appears to be more luck than anything else.
Why did all of the engineers volunteer? And why would Dagney leave the selection to chance?