Depends on which writer. There are instances of Thor using Blakes' skill. There are instances when he changed back to Blake to perform surgery especially in the Lee\Kirby years. However I do not know if that was because Thor lacked the ability or in order to protect the identity plus a god in the hospital would bring a lot of questions. Have you read the early stories or only the post Lee depictions. I envy people who are reading them the first time.
I am thinking of the time Set appeared to fight Thor, and he was doing surgery as Blake, and too charge, as he commanded the nurses to keep their heads and finish the task at hand!
Think Blake used to ground Thor to humanity, yop ber his "Clark kent:, and also to have his Green K weakness as being the 60 second change back if hammer was removed!