Over the years, Rick Hahn and the White Sox have been slow to churn their bench. Occasionally, a guy does bad enough that they are eventually sent down to AAA or rarely DFA'd, but the fans have had way more than enough of a player before they are finally sent away.
Looking at Alex Anthopoulos's time at the Blue Jays is almost completely foreign compared to the White Sox. The last few guys on the Blue Jays' roster was continuously in flux as was their AAA roster. It's almost been a bit of a joke that when someone is DFA'd, they seem to end up in Toronto. The joke might be on everyone else though as some newer portfolio theories suggest that it's better to being active might be better than being good.
It all comes down to this formula that's the basis for Active Portfolio Management.
IR = IC × √ Breadth
Let's explain a few things here. IR is the information ratio. This represents the excess returns essentially from a portfolio manager or a GM. IC is the information coefficient. This is a coefficient of the forecast to the actual return. Finally, breadth is the number of transaction opportunities. Another way to think about this formula is to look at it like this.
Performance = Skill × √ Opportunities
Looking at it this way, there aren't a lot of ways for a GM to improve their skill. They can get better analytics and get better models, but this part of the equation is mostly constant. So for a GM to show off their skills, they need to make transactions, and the more transactions they make, the more their overall performance improves.
This probably takes everything you've heard about "buy and hold" and throws it out the window. Also, because of the guaranteed nature of many baseball contracts, it makes it difficult to churn the portfolio that much. That said, there is certainly room to make moves at the end of the bench.
We've all seen the White Sox version of "buy and hold". A new position player is called up and he just lights up the league. Over time, though, he gets more exposed to the league and the league eventually learns how to take advantage of this player and their performance degrades. With more active management of the roster, a player would be moved out the second that it seemed like the league was catching up with the player. Instead of relying on the player to make the next adjustment, the league would have to adjust to yet another player on the team.
As you can probably see from the math, if a GM has a negative skill, being more active with the roster will turn bad quickly. All you have to do to verify this is to take a look at the 1986 White Sox.
Overall, being more active isn't going to suddenly turn a AAAA guy into Mike Trout, but if the White Sox could grab a few extra couple runs a month just by rotating the end of their bench a bit more aggressively, it could turn into an extra win or two a year. That combined with a few additional good players could make the Sox looks a little more like a contender.