In theory, I hear you. I do think about the bullpen - for sure. Unless you have a good idea your pitcher is going 7+ innings, you think about things like that. Gagne, Mariano (2 of the best closers in the game), Borowski, Foulke, Mantei to name a few.
In my other league, we pick pitchers - not pitching staffs - and hang on to them. DB prob does the same in his rotisserie league. That is a whole 'nother game; whole different ball of wax, whole different strategy.
If you are suggesting we change up the game a little at this point,then no, I am not in favor of that. I think it is hard enough to keep players in this game (all 7 of us )and if you complicate things up they'll leave in droves.
And it would be no fun playing with yourself, would it?
But then again, I am just one voice. I can go with the flow - but remembering, I too will often have to be a member of the "set it and forget it" club. And then your idea would sure suck. Blow chunks. Suck ass.
I have a tendency to wear my heart on my sleeve - I have a history of taking off my shirt.....