However, once the playoffs roll around each fall, managers abandon this pattern in favor of getting their best arms on the mound in critical situations. The ace of the staff is expected to start twice in a 5-game series and potentially three times in a 7-game series. Closers are asked to record saves longer than an inning. Middle relievers are all but abandoned in favor of the 4th and 5th starters who probably have better stuff, the trade-off being their
Coaches of any sport will tell you that the best preparation for performance when the game is on the line (short of actual experience) is...practicing the technical situations associated with a game on the line. Baseball is a 162-game season with an average of one day off per week. The sport is not inherently conducive to practicing game-like situations, nor is there much time during the season for practice of any kind. Batting practice is part of a daily regimen most critical for allowing hitters to acclimate to the visual cues of the backdrop behind the pitcher in order to better pick up the rotation of the pitches that evening. Starting pitchers take one session between outings to keep their arms in shape and work on any mechanics that might require tweaking. Relievers, on the other hand, languish in the bullpen until they are called upon, and may certainly get in some work to stay sharp, but are, in general, not experiencing a regular daily workload.
The six-man rotation has often been discussed in various configurations as a way to rest the stronger starters. However, the economics of paying another starter and not getting as many starts out of your top 2–3 arms seems to be a barrier to implementing such a strategy. What if the work between starts were live, and not in the bullpen? What if, on every third day after a starter had his turn in the rotation, he were considered available for long relief? If that day's starter threw a gem, he could get his work in in the 'pen. If not, he would come on for a relief outing equivalent in pitch count to what he would have thrown anyway. The ~40-50 innings lost to an ace having only ~27-28 starts instead of ~35 would likely be made up for in quality ~2-inning outings in relief that are more than marginal upgrades from those same innings being thrown by dedicated middle relievers.
The pros: better quality middle relief leading to a lower average pitch count for starters, more realistic playoff preparation, more consistent organizational pecking order.
The cons: fewer innings as a starter for the ace, new routine to learn for starters, fewer opportunities for technical tweaking after a rough start, potentially a new conditioning regimen needed to manage arm health.
Fundamentally, pitchers are going to be starters, closers, or guys aspiring to one or the other. Nobody is sitting in AA or college thinking, "I can't wait to pitch 2.1 innings once or twice a week for the Pirates." The guys with the competitive drive to make it all the way to the show are for the most part required to wait their turn and establish themselves through effective middle relief or set-up duties before earning a spot in the rotation or a job as a closer—no pitcher views the positions that seldom record more than outs, holds, and blown saves as terminal career stages.
So...if a manager is going to eschew middle relievers in favor of late-rotation starters in the playoffs anyway, why not just use them that way in the first place? Not only will the routine be more familiar for all involved, but the added roster spots could be used to add a second specialist and closer. A team using twelve roster spots on pitchers could carry: 6 starters, 2 specialists, 2 set-up guys, and 2 closers, and feel confident that they have an advantage in the late innings as well as a lot of flexibility in case the starter has a rough night.
Why add potentially expensive redundancy to the bullpen? Curious is the practice of pitching relievers in the same order regardless of where in the lineup the opposing team may be. If the trailing team has 2-3-4 due up in the 8th, should a manager go to the set-up man, saving the nominal closer for the 5-6-7 (or most likely 6-7-8 or worse) for the 9th inning? Does it not make more sense to send the best bullpen arm out against the opposing team's best weapons in the 8th, and then let the second-best arm finish the game against the bottom of the lineup? Sure, this would screw with everyone's fantasy league stats (I will refrain from going into a rant about the stupidity of fantasy leagues for now), but, if the set-up man comes in and retires the heart of the order, leaving the closer to annihilate the two weakest hitting position players and a pinch hitter in the next frame, which pitcher deserves the save?
On the road, with the opposing fans creating a atmosphere designed to propel the home team to a comeback, the mental aspect of closer vs. set-up man may supersede the logic of matching up the best guy against the meat of the lineup. That 7-8-PH batting order with 30,000 charged up fans behind them at home in the bottom of the 9th—with each pitch out of the zone sufficient to incite a roar—may be a more formidable opponent than the same batters attempting a comeback on the road in the top of the 9th, where each strike brings more fans to their feet in anticipation of a joyous ride home (or joyous 90-minute parking lot 1.2mph average speed caravan dodging firecrackers thrown by disgruntled Met outfielders while leaving Chavez Ravine, but I digress).
Furthermore, many managers will send their closer out in the 9th inning of a tie game to keep things under control, but then are forced to either continue pitching that guy in the 10th or go to a lesser arm. The former situation is a mental disconnect from the closer's usual job description and is likely only to be effective if the hitters due up in the 10th are mediocre. The latter manages the closer's workload but gives the opponents a greater chance at victory. With the extra roster spots gained from obviating the need for dedicated middle relievers, a second closer could be carried to mitigate both scenarios, especially on the road, where a team must pitch its way out of the bottom of the last inning and certainly doesn't want a guy who isn't good enough to start or close trying to protect that lead.

While a small-market team may have the youth and organizational depth to implement such a rotation, it's probably more likely that a big spender would overpay for the extra starter and closer necessary to make this happen. But, the benefits go beyond rotation flexibility and more realistic playoff preparation for managers: young pitchers would be closer to their target career stage and be directly competing for the respective spots at either end of the bullpen bench. Even better, the "hold" would have to be retired as a mostly useless stat, replaced by ranking relievers the only ways they can be ranked meaningfully: outs, outs per appearance, and outs per batter faced.
The economic barrier to carrying an extra starter and closer instead of two nondescript middle relievers is obvious, exacerbated by the fact that there may not be enough depth in the talent pool to even make such a move. However, if a team consistently brings pitchers up through its farm system with the understanding that they will debut in middle relief before establishing themselves as either starters or closers, the pipeline should achieve steady-state, and the pitchers who would take over in the starting or closing rotation should a starter or closer falter are already on the big club, next in line.