Letting politicians form relationships over a certain amount of corruption sounds more like a worst case scenario to me. If the only way we can get them to negotiate or relate to one another is through back-room power brokering and trading political favors (especially patronage) then that's just the public losing out on both fronts. The gridlock is bad, but the dirty dealing are worse, since in neither case can we trust the politicians to have the public interest at heart. Partisan gridlock is about not being willing to compromise your ideals for even the right reasons; dirty dealings are about being willing to compromise your ideals for all the wrong reasons. So you're basically outlining either no compromise or the wrong kind of compromise.
Granted, I think the depiction of the two party system as two sides at each other's throats constantly is an over-simplification. The Dems and the GOP each have a stake in keeping the other in power, and that's the reason they compromise at all, because they know that in the long run, they'll always have a turn in power or a chance to beat them in the next election. If third parties start cropping up everywhere, that security disappears, and so they both work to protect each other in that regard. That's when things actually get done, and while it's not ideal, it at least has an air of transparency to it that outright corruption and dirty dealings do not. I'd rather have ideological extremists on both sides, than amoral political animals running wild.