Interesting notion, but after thinking about it for a second, for some reason, I started to think about probablities and statistics. I think one of the problems with this strategy is that the more pitchers you use in a game, the more you put the team in risk of one of those pitchers having an "off-day". A Manager would have to use 2-4 pitchers most likely to compensate for a starter. Even if your starter has a much greater chance of an "off-day" compared to each reliever individually, this can still work against a team.
Just to make it easy, let's say to compensate for the innings a starter will pitch, a Manager must use 3 relief pitchers. And say your starter has a 50% chance of a good performance (conversely a 50% chance of a bad performance), while each reliever has only a 75% chance of a good performance (25% chance of a bad one). The probability of all three relievers having a good performance would be:
(If I remember correcly from stat class, i think I do)
(the probability of relief pitcher A having a good performance)
(the probablitiy of relief pitcher B having a good performance)
(the probablity of relief pitcher C having a good performance)
Since they all have the same probability of a good performance you raise this to the thrid and get: (3/4)^3= .421875 or roughly 42%.
This shows that even though each individual relief pitcher has a (much) higher chance of a good performance(75%) compared to the starter(50%), cumulatively, the relief pitchers have a worse chance of all
having a good performance; 42% compared to 50% .
Obviously this is a very simple example, with "everything else held equal", but I think it does illustrate some of the logic behind why this strategy isn't used in baseball.
I hope I got this close to right