Past history will suggest...NFL Owners should keep the system in place but, get a "New Head Coach". Replace the Head Coach with a less expensive, inexperienced, candidate seems to be a successful trend for past Superbowl winners!
Tomlin, Coughlin, Gruden, Billick, Vermeil and Seifert. I'm sure the experts of SBR can provide more accurate data but, I think Vermeil was also a new hire but, obviously experienced like Coughlin. If I recall, Jimmy Johnson's experience was mainly College (Miami) and won Superbowl's fairly early in his NFL Head Coaching debut.
My point is...Indy's Caldwell falls into this category of becoming a "New Head Coach", keeping a system in place formed by Dungy (as did Gruden) and maybe on the doorstep of a Superbowl Championship.