There are two parts to the answer.
The first, and easier, part is: supply and demand. The current market demands that, to be competitive in hiring a good coach, schools and NFL franchises have to throw the bank at him. Generally speaking, the supply of $$ is no problem at the top end of the sport, so buyers of coaching staff are willing to play along. And that bank they throw the coach's way better include a golden parachute. If they don't spend that much on him, someone else will.
But that part doesn't really get to the root of your question. You know that's how it is now. But what you're really asking is how did we get to this point? And I have no idea of any of the particulars. I mean, we can easily guess that it happened incrementally. One coach and his agent, out of nowhere, said: I'd like to be guaranteed income even after I leave the job, to cover me until I find a new one. And the school or NFL front office wanted him bad enough to agree. And then other agents and coaches heard about that contract and started asking for the same. And the schools and front offices, they had TONS, I mean tons, of dollars flowing in from the popularity of the sport, so they saw no good reason not to go with the trend.
So we have a general idea of how it must've evolved, but I've never seen any article or story with a detailed breakdown of the evolution over time. It could be a good read (or, with the wrong writer, it could be like reading tax returns). Someone good should research and write it.
Anyway, at the end of the day, it's just supply and demand. And when it comes to coaches, it's a sellers' market these days.
p.s. Most of those CEOs you mention, whose continued employment is tied to performance metrics (just like coaches, btw), they also have golden parachutes. This practice is not unique to sports, and didn't even start there. That football coach who did it first, he probably got the idea from some CEO.