The problem with getting rid of pork-barrel spending is that it removes the one incentive for reps to cooperate on legislation with people they'd otherwise oppose. The only remaining force in legislation post-pork-barrel is ideological extremism.
This is a pretty poor solution for trying to get people to cooperate. If people are opposing good legislation just because it is being proposed by "the opposition", then the system is broken. Better to solve the problem directly, rather than some unplanned round-about solution with pretty clear downsides.