United States history up until 1863 demonstrates that successful generals make good Presidential candidates. Lincoln would have been foolish if he had not taken that history seriously. With respect to Grant, it took some time for Lincoln to satisfy himself that Grant had the job he wanted and his hands were full trying to do that job. Any thought of the Presidency would have been based on some unexpected incapacity of the President.
The pressure in the Midwest and in Congress generally, to do something about the war in the eastern theater was tremendous. All four appointments in the east were political. Sigel was a German immigrant. Grant was the most popular Midwesterner. Butler was a war Democrat. Sheridan was the son of Irish/Catholic immigrants. Grant over shadowed Meade and Hancock, who were McClellan men. If one poked around in the Navy appointments, the same pattern shows Dahlgren getting the key south Atlantic squadron.
Lincoln treated Grant well. While he only released control of the war to Grant in pieces, he sustained Grant through four months of the worst war news that the US was to experience until after Pearl Harbor.
Lincoln allowed Grant to get rid of Smith, and then form a unified command under Sheridan to take over defense of Washington, which was a large indulgence of faith. Lincoln and Assistant Sec'y of the Navy Fox then were able to inform Grant that the long asked for operation to close Mobile Bay was ready to proceed. Then Lincoln approved a temporary leave for Burnside, which became permanent, which was a difficult by necessary change.
Lincoln made the most of Grant's small steps in severing the Weldon railroad and then staked his Presidency on Sherman's right wheel around Atlanta.
It took some time, but eventually Grant got most of what he wanted and everything he needed and the risks paid off.