Some argue that the Lincoln government would have fallen if Lincoln had not acted tough at Sumter. Maybe, maybe not. The attack on Sumter actually served the immediate objectives of both sides. Lincoln got patriotic support from Northerners upset over the attack on the flag, and Davis got border and wavering states to join the Confederacy.
As I've mentioned before, in spite of what he was advised was required, Lincoln didn't put near enough resources into his fleet to make the relief effort work. He didn't need to win -- he only needed to make the effort. If he lost at Sumter he could use an attack to rally the North behind him and get the support he needed to govern.
It was something that the CiC simply had to do!
No, he didn't.
Logically, doesn't that presuppose that Lincoln would have been prepared to either see Sumter relieved, or been willing to use the Navy to pound Charleston into submission?
It appears that Lincoln's intention (actually hope) was to deliver supplies to Sumter and thereby maintain the status quo and his best chance of doing that was sending a small force that was obviously not threatening. If he actually was intent on war, logic would dictate that he do as you suggest and send a strong force.