A team can never have enough minor league talent, even for a good farm system. Consider the recent history of Boston Red Sox prospects. At one point they had one of the more loaded systems in baseball, and it featured Xander Bogaerts, Jackie Bradley Jr., Will Middlebrooks, and Jose Iglesias. This isn't a bad system, and I still would stand by that now. But considering all of these players were pegged as feature regulars or superstars, I wouldn't say it lived up to the hype. Bogaerts has yet to live up to expectations, Bradley is a fourth outfielder in for defense, and both Middlebrooks and Iglesias have been shipped off for modest returns (Ryan Hanigan and Jake Peavy). So while a system like this can produce a lot of depth, you're not going to get multiple stars. The Red Sox even went out and acquired Yoan Moncada, and that speaks volumes for a team that "should" produce multiple stars.
And this is why it is imperative for the Yankees to acquire as much talent as possible. As I said, that's the case for every team, but this is not a loaded system. When you have the wealth of depth, you can still get away with a less than median outcome and get a few nice pieces, but the Yankees essentially have a couple of very good prospects, and a lot of fringe types. However, if we were to bring up specific needs, there are a few positions that come to mind.
Pitching would be the first. In particular, starting pitching is a horrendous weakness for the drafting and player development squad. In recent history, the Yankees have only produced Phil Hughes and Ian Kennedy. That's pretty much it. The Yankees currently have Bryan Mitchell, who could at least make it as a back-of-the-rotation starter, and there is of course Luis Severino, but that's about as far as upper-level pitching talent goes. In the lower levels there is Ty Hensley and Ian Clarkin, but Hensley underwent Tommy John surgery, and Clarkin is currently on the disabled list due to "elbow inflammation." Great.
There are a lot of flawed pitching prospects in the middle of the first round, but there are a few that could escalate through the minors as potential starters, such as Walker Buehler, Cody Ponce, and Nate Kirby. They're all a bit risky, but they are the type of higher-floor college pitchers that would fit better in an organization that struggles to produce starting pitchers.
There is also an obvious need in the middle infield. In the upper levels of the minors, there is Rob Refsnyder. That's it. In the lower levels it is a bit better, but these players are many years away. There is Jorge Mateo, the potential star shortstop with 80-grade speed, and the July 2nd prospect in Dermis Garcia. They are both incredibly young, so don't expect to hear about them coming to the big league level for another few years (if ever).
There are actually a few shortstops (or second basemen, depends on which scout you hear it from) in the first and second rounds that could be potential targets. There is Kevin Newman, arguably the second best college bat in the country, but a lot of scouts don't think he falls before tenth overall. There is also Richie Martin and Kyle Holder, but they are a bit more on the fringe.
Another position of need is catcher, and that's one that I'm actually not too worried about considering their development staff. The Yankees are particularly skilled at curating adequate catchers, and they have two decent ones in the minors in Luis Torrens and Gary Sanchez. A year ago I would say their depth is fine (especially considering John Ryan Murphy), but that has since changed. Sanchez has continued to show little progress on both sides of the ball, and Torrens is out for the year due to shoulder surgery. And with Murphy graduated, that leaves little depth to work with.
Catching prospects in the draft are pretty thin, but rumors have been swirling that the Yankees were targeting Tyler Stephenson for their 16th overall pick. I would be fine with that, except that the Diamondbacks may try to sign him under-slot at first overall (!!!!). Other than that, there is really just Chris Betts, and a catcher with a plus arm and raw power is fine with me, even if he doesn't cut it defensively.
The depth at corner infield, outfield, and bullpen are adequate, but it could always use work. The corner infield has Eric Jagielo, Greg Bird, and Tyler Austin, and that is fine, at least for now. The outfield obviously features Aaron Judge, and then there is the depth pieces of Ramon Flores, Jake Cave, and the lower level prospect in Juan De Leon. And the bullpen obviously has Tyler Webb and Jacob Lindgren, but there are always decent picks available (with two plus pitches) that could be harnessed into decent relievers. The Yankees have shown that they're adept at that.
Other than a few areas of just-barely-decent depth, the Yankees have needs everywhere. The top portion of this draft is pretty poor, so this is the year the Yankees need to fill in depth with some savvy lower-round picks. As draft day approaches, the team's targets will surely come into focus.