Washington, Jefferson and Lincoln were the consensus "greatest presidents" at the time construction began in 1927. Teddy Roosevelt was an old friend of the sculptor.

Source: One Summer - 1927, America, by Bill Bryson:

For his subjects [Gutzon ]Borglum selected Washington, Jefferson, Lincoln and – to widespread consternation – Theodore Roosevelt, who was chosen, it seems, not for his greatness but because he and Borglum had once been chums.