The question was whether we'd have had a war if there hadn't been slavery. Are you arguing that the South wouldn't have seceded? Or that that Lincoln wouldn't have started the war when the South seceded without slavery?
I'm suggesting that the South might still have seceded without slavery, but there would have been a more difficult time for Lincoln to invade if there hadn't been slavery.
It gave the Union an eventual "moral" excuse to invade the South, and eventually carpetbag the means of production by taxing the burned out properties away from their owners*, provided the owners even survived the war.
Slavery was a convenient smokescreen for their economic motives, and it remains that smokescreen to this day. Had slavery been the seminal issue, why did Lincoln wait until 1863 to try to free the slaves in the South with a proclamation over an area over which he did not have authority? If this was such an issue, it should have been first and foremost, right from the git-go, and that attempt should have been the first shot of the war.
(*Back taxes were also used as an excuse to steal over ten million acres from my wife's people, too. Great system to steal land with. Not so great if it is your land being stolen.)