Why didn't Davis do the same?
Are you forgetting about the Confederate Commissioners to the United States nominated by Davis on February 25, 1861, and unanimously approved by the Confederate Congress? Those same commissioners that were later lied to by the Lincoln Administration concerning the evacuation of Fort Sumter? The same ones who on April 11 called the Lincoln Administration's deception about Sumter "gross perfidy?"
Here is what the commissioners sent Seward on March 12, 1861 [my bold]:
WASHINGTON CITY, March 12, 1861.
Hon. William H. Seward, Secretary of State of the United States.
Sir: The undersigned have been duly accredited by the Government of the Confederate States of America as commissioners to the Government of the United States, and, in pursuance of their instructions, have now the honor to acquaint you with that fact, and to make known, through you to the President of the United States, the objects of their presence in this capital.
Seven States of the late Federal Union, having in the exercise of the inherent right of every free people to change or reform their political institutions, and through conventions of their people withdrawn from the United States and reassumed the attributes of sovereign power delegated to it, have formed a government of their own. The Confederate States constitute an independent nation, de facto and de jure, and possess a government perfect in all its parts, and endowed with all the means of self-support.
With a view to a speedy adjustment of all questions growing out of this political separation, upon such terms of amity and good will as the respective interests, geographical contiguity, and future welfare of the two nations may render necessary, the undersigned are instructed to make to the Government of the United States overtures for the opening of negotiations, assuring the Government of the United States that the President, Congress, and people of the Confederate States earnestly desire a peaceful solution of these great questions; that it is neither their interest nor their wish to make any demand which is not founded in strictest justice, nor do any act to injure their late confederates.
The undersigned have now the honor, in obedience to the instructions of their Government, to request you to appoint as early a day as possible, in order that they may present to the President of the United States the credentials which they bear and the objects of the mission with which they are charged.
We are, very respectfully, your obedient servants,
JOHN FORSYTH
MARTIN J. CRAWFORD
And from the resolution passed by the Confederate Congress concerning the negotiations [my bold again]:
Resolved, etc., That said commissioners be further instructed to present to the Government of the United States assurances of the sincere wish on the part of this Government to preserve the most friendly relations between the two Governments and the States comprising the same, and to settle, by peaceful negotiations all matters connected with the public property and the indebtedness of the Government of the United States existing before the withdrawal of any of the States of this Confederacy; and to this end said commissioners are hereby fully empowered to negotiate with the Government of the United States in reference to said matters, and to adjust the same upon principles of justice, equality, and right.
Old peace loving King George Lincoln wouldn't even meet with them to tell them to go jump in the lake or that he wasn't going to let them go because he needed Southern revenue to run his government. Instead, Seward reassured them that Sumter would be evacuated, and Lincoln's agent Lamon did the same with the Governor of South Carolina.