The Kevin Youkilis trade--and his just dandy .277/.373/.479 line with the White Sox--plugged the last truly awful, burning hole amongst the starters. At 3rd base, there was injured youngster who was terrible, there was veteran fill-in who was terrible, and significant salary commitments to neither. It was perfect situation to add a veteran rental, and it was coupled with the perfect situation where a talented veteran was available and had his value depressed by flukish poor play, injury and loss of his starter spot.
Basically, it was the perfect storm of trades, and it's hard to imagine it happening again. While the White Sox appetite for adding to the roster has not diminished, the spots have gotten less obvious, and the standards have gotten higher.
Where there's room for improvement
2nd base - For a second there, Gordon Beckham was hitting in the #2 spot, and hit, well, not good enough to deserve the #2 spot. He hit .264/.311/.410 in 196 plate appearances there, and that nearly league average hitter has completely disappeared since Kevin Youkilis arrived, as Gordon has compiled a .169/.225/.241 line since. A lot of that is bad batted-ball luck, and when Alexei Ramirez is the only hitter having as bad of a season as him, he can't really make an argument to move up.
Beckham's a poor hitter, but a good gloveman at an up-the-middle position, which makes it a fair bit harder to find someone with a bat worth bailing on him and his long unfounded potential for.
Left fielder - Dayan's wacky combination of raw power, off-balance lunging and wild swinging has produced an exactly league-average hitter (99 wRC+). That's not great for a left fielder, but it's fine for a 23 year-old that was expected to develop as the season wore on, especially since he's been just fine in left field. He's not a star, but figures to be an asset going forward, making it even harder to find a worthwhile upgrade than it is for Beckham. Perhaps if Justin Upton was coming on the other end of the deal it'd be worth it, but he isn't.
Starting pitcher - We all have coins in our pockets more reliable than Philip Humber and Gavin Floyd have been this season. Waiting for Gavin to trend in the right direction at the end of the rotation is fine, relying on the two of them is a rather dodgy place to be. That's what John Danks' recovery is for, but that's a month away at least. It's pretty lean in the mean time, especially if Jose Quintana falls back to Earth.
Relief pitcher - This bullpen still has Leyson Septimo in it as a third lefty. It can be upgraded.
It's not like Humber and Floyd have no business being the major leagues, or they're relying on Dylan Axelrod and need an innings-eater. So as Kenny Williams searches for a way to make an impact, there's a need to go big or go home, hence the interest in Greinke.
But that's also where the complete lack of worthwhile prospects comes in. The only reason ever given why the Sox are candidates on any big-ticket trade candidates are because "they really want him" or "Kenny is unpredictable!"
That's not a whole lot to go on, and cheaply improving the bullpen again seems the logical and actually achievable road to travel.
Waiting out for rebounds from veterans, and small, no-risk trades have brought the White Sox to the precipice of playoff contention. But now that the mid-season rush on spare talent is on, the lack of prospect depth is really getting exposed. The only super-impressive prospect in the system can't be traded because he's this year's 1st round pick, and patronizing excuses like "well, they all graduated to the MLB team" don't work when the big club still needs help and the minors are unable to provide it.
It's a predictable end, yet simultaneously unfathomable, since a team typically rolling in pitching depth is looking to upgrade the rotation, and have no obvious spaces to add a bat in a shockingly decent lineup.