Executive Producer Sera Gamble picked up the reigns for Season 6 and 7, and then Jeremy Carver assumed the role in Seasons 8-11.
Supernatural has been running for 12 seasons and in that time its changed a lot of hands.
Eric Kripke served as showrunner from Seasons 1-5 before stepping down.
I can’t imagine there are many longtime fans who would be opposed to this idea, and it really would be a great way to cap off the longest running fantasy series on television.