Why didn't Lincoln just let South Carolina have Ft. Sumter? Why draw a line at Sumter when you allowed the Confederates to take over other US installations throughout the South?
You don't let them have the fort because you are going to force their hand... and the South was a willing and complicit partner to having their hand forced.
First of all, Lincoln did not allow the confederates to seize federal facilities all over the south. Buchanan did that, and Lincoln was in record as opposing it. In several speeches prior to the inauguration, and in his inaugural address itself, Lincoln had stated his position that the U.S. would continue to retain those facilities belonging to it that had not already been seized by the Davis regime. And why not? Sumter was federal property, built by the federal government on land deeded to it by the South Carolina legislature, and the Davis regime had no claim to it.