Actually he would have anyway. Lincoln won in 1860 with about 40% of the popular vote but with about 60% of the electoral vote. With the exception of California and Oregon, Lincoln took all his states with an absolute majority of all votes cast. So even if the Democrats had stayed united and had taken the west coast states Lincoln would still have won with 173 electoral votes.
You're correct, of course, at least in theory.
But elections, then as now, are like military battles in that they sometimes depend as much on the enthusiasm and devotion of their troops to turn out the vote as on raw political calculations.
I'm saying that when the South split up the Democrat party, they dispirited those who could have helped them the most, and thus suppressed the pro-slavey vote.
After all, in 1860 the anti-Republican popular vote totaled 60%.
If you ask, "why would they commit such political suicide?"
the answer is: because that was actually preferable to the economic suicide which would result from remaining in the Union -- while even the Northern Democrats favored slowly, slowly, slowly strangling slavery in its cradle, so to speak.