Fantastic question! If Issac had left the show for more common reasons (wanting more money, wanting to take other big roles, retiring), they probably would have done something like what you suggested.
However, Hayes actually left because of the "Trapped in the Closet" episode from season 9. He was a Scientologist, so you can at least understand why he wouldn't want to work with a show that openly bashes Scientology. To record even one more episode with the studio could have potentially hurt his reputation with his Scientologist friends.
But the writers of South Park are far too hardcore to let one of the show's most famous characters just disappear, so they brought the character back one last time in any way they could imagine.