If we saw the Yorktown, and she was a Connie, I would be more inclined to consider it. As it is, we have no idea what class that ship was. How far from Earth was she, I wonder? I just always pictured that as one of the lesser vessels, for some reason.
Yorktown was a World War II aircraft carrier, and the original name for Trek’s starship. I can’t imagine the intention was for it to be a lesser ship.