Not necessarily there was no one to promote. Cooter a 2nd time? Our DC?
When it comes time to fire someone, there are always available options. No company has ever not fired a failing employee because they didn't have a viable immediate replacement.
If you feel the guy is detrimental to your company, you fire him before he can do more damage. You fire the coach before he gets an expensive long term investment like Calvin Johnson or Matt Stafford injured.
We're not just talking about the wife who inherited the team. We're talking about a woman who grew up in boardrooms spoonfed the fundamentals of business by the time she took her first steps. She knows how to run a company and showed that by firing Mayhew and Lewand (and according to some reports, many many other people who's names weren't important enough to make the headlines).
She either believes he's a good coach who can turn this team into a championship team, or he's too expensive to fire right now.
According to Coaches Hot Seat, he's the 27th highest pain coach in the NFL, but that still comes at a price tag of $4Mm per year, and he's only in the 2nd year of his 4 year contract.
http://coacheshotseat.com/NFLCoachesSalaries.htm
To fire him now during the purge (love that, I'm just going to call it The Purge from now on) you would eat $10Mm while having to find a new coach and likely pay him even more, making your head coaches position more expensive than Sean Payton at $8Mm a year.
My guess is Caldwell is here in 2016, and then maybe fired after 2017 if the improvement isn't there. Almost all of these coaches have a buyout clause in the contract, so when the buyout becomes less expensive than the contract, you pull the trigger.
Only in the most dire of circumstances would he be fired during the season due to the money, and likely it would take a catastrophe of epic proportions to get him fired before year 3 was up.