There are two checks against the agreed upon "right thing",the national executive who has to agree with the consensus, and (thanks John Marshall), a system of (theoretically) impartial courts which can decide if the "right thing" is actually allowed according to the rules of the game (Constitution).

The slavery compromise was exactly that. First the 3/5th agreement, then the Missouri compromise, then finally, when one side got all of the power (which is what the system is supposed to mitigate the chances of) a shooting war.

Lincoln likely wouldn't have gone quite so agro on slavery if not for succession.

And there likely wouldn't have been a United States if there hadn't been any compromises on slavery. The two sides would have split at the outset, and either 1) neither would have been able to amass enough influence on the continent and they'd have been reabsorbed by a European power 2) after a hundred years of independent growth and simmering hatred, the two nation's would have had a war even more disastrous than the American civil war.

Moderate political solutions are (1) very frustrating and (2) much more effective in practice than they have any right to be. Often both sides of a political argument are wrong about the nature of reality and a solution where the major concerns of both sides are addressed is pretty good.

And the important thing is often that decisions don't happen in isolation. A moderate middle ground solution that fails often lends a lot of weight to the next round of negotiations when people decide what to try after compromise solution #1 fails.

The moderate solution failing probably isn't going to be as catastrophic as a unilateral solution from either of the opposite ideological camps.

The system survives long enough to make it to the next round of negotiations

It's not great, but it sucks the least.

Which, given that the US Constitution of "minimize the damage one person / group can do" is the longest standing constitution currently, I think it's one of the better solutions.