There are several reasons Republicans, and most notably Lincoln, rejected compromise:
It included the extension of the MO compromise line to CA, something they steadfastly rejected (Free Soil, Free Labor, Free Men).
It would have forced Northern States to more rigidly enforce the fugitive slave law.
Most important, it would have dissolved the Republican Party. Lincoln would have been a one-term president and a man without a Party in four years.
It must be noted that Jefferson Davis and Robert Toombs as important members of the Committee of 13 supported the Compromise and only switched their votes to reject it when all Republicans on the Committee (5), at Lincoln’s insistence, voted against it.
Yes, it would kept all the other Southern States in the Union. Only SC was out at that point. Lincoln could have saved the Union had he wanted to do so in December 1860 by giving his support to the Compromise. This is why Lincoln’s rhetoric is hollow.
Lincoln generally opposed any compromise during the Secession Crisis, as he insisted that secession was mere bluster and that nothing substantial would come of it. His election signified the right to rule, he said, and he would exercise that right. Michael Holt of the University of Virginia calls Lincoln’s performance during the Secession Crisis the “nadir” of his statesmanship. I had occasion to write about this recently:
Professor Gutzman, excellent article! I hope that maybe there will be more lectures on the War for Southern Independence in the near future. I always wondered why they couldn’t come up with some type of compromise to keep from going to war that killed so many people. If they avoided going to war before over the tariff issue why couldn’t they this time?
My reading is that Lincoln didn’t want to avoid it. Take a look at Crofts’ RELUCTANT CONFEDERATES for incoming Secretary of State William H. Seward’s desperate efforts to patch together a way to avoid war.