First of all let me point out that it does not appear that any other team had any interest in Culver as a first round pick. Baseball America rated him as the 168th best prospect in the draft and he was not even mentioned in Keith Law's top 100. If they Yankees really loved Culver, they probably could have gotten him in third round, or even later, and spent the first round pick on someone else.
The truth is that we do not know what type of player Culver will be, and we won't know for a couple years either. What we do know is that the Yankees have been trying to draft Jeter's eventual successor for several years now and have had shockingly little success. Let's take a quick look at all of the shortstops they have drafted in recent years, and how things have worked out.
2004 Nate Phillips (6th round 150K bonus) - Phillips was never a big prospect but got an over-slot bonus after being drafted from a Texas high school. Phillips never even made it to full-season ball.
2005 C.J. Henry (1st round, 1.57M bonus) - Henry was an athlete that the Yankees thought they could turn into a baseball player. In a draft that was absolutely LOADED with high school hitters, the Yankees completely whiffed, drafting a player who never made it above A-Ball.
2007 Carmen Angelini (10th round, 1M bonus) - The Yankees loved the athletic Angelini, but hte consensus at the time was that he would never hit enough to make it to the majors. Now in his third full season, Angelini has an OPS of roughly .500 in A-Ball.
There are other players like Addison Maruszak, Garrison Lassiter and Corban Joseph who were drafted as shortstops but have now moved to other positions or failed to hit. But let's focus mainly on C.J. Henry and Carmen Angelini.
Both of these players were not considered elite prospects in the draft and the Yankees clearly thought more of them than the rest of baseball. Both of them had questions about their and both of them COMPLETELY FAILED. Neither of these players ever gave even the slightest impression that they were a major leaguer. They could not hit at all.
The point is that Culver is the exact same type of player as Angelini and Henry, with the Yankees reciting the exact same verse about how much they believe in him. I'm not buying it. Derek Jeter was considered a top prospect by everyone when he was selected 6th overall, and the Yankees are only fooling themselves if they think they that his eventual replacement will be a player that no one else wanted.