What you describe seems to apply more to a starting pitcher than a reliever who comes into a game knowing the time is limited to find that "groove." And that's not even the leading reason for all MLB manager approaching the bullpen this way. A huge, big, important reason is to keep that pitcher available for multiple days to come because if you're going to make decisions on the hot hand and the length then you'll quickly see the bullpen come undone -- and be unable to minimize damage. We can go through an example of this.
Say a team has three relievers it trusts to hold a lead, and it took your approach.
Pitcher A gets hot, throws 2 1/3 innings (30+ pitches), closes out Monday game.
Tuesday comes, Pitcher A is not available.
Pitcher B goes in, struggles in the seventh, gets only two outs. Leave seven to get.
Pitcher Closer comes in to handle that, rescues, team wins Tuesday.
All three pitchers are now possibly unavailable for Wednesday.
Or, if Pitcher A or B is available, there's no safety net.
Let's also consider that the way the bullpen is used now is how those players train. They are focused on work that keeps them ready for 15-20 pitches on back-to-back days, and when necessary back-to-back-to-back days. If you starting varying that then you also start varying how they prepare. Does every pitcher need to be ready to throw 35-45 just in case this is the night the manager wants to ride them to the save/game ending, as you suggest? Right now, Reyes, Gallegos, Helsley, and Cabrera have a good feel for what will be expected from them night to night and how to prepare for that. They also know how to get ready for that one inning and be as right as possible in it.
Change that and you're changing how they prepare, how often they can prepare, how often they can pitch, and likely the results will be as varied as their usage in your scenario.