You would never fire a coach who just got his team to a SB, but IMO Fox's spectacularly poor preparation for XLVIII was a fireable offense. I think that performance put him on thin ice.
I think John Fox is basically the same coach as Mike Smith. Watch him talk to his players and you can easily tell that he's not a leader of men. I don't think Falcon's players respected Mike Smith and I don't think Fox's players really respect him either. I'm sure they are okay with him, but he's not the kind of coach that players would bleed for.
Smith and Fox are both coaches with defensive backgrounds who posted winning records despite mediocre game preparation thanks to having a franchise QB. At least Fox can point to some good defenses over his tenure, but he's mostly felt like a figurehead, not a difference maker.
As far as letting the whole staff go, that's probably evidence of John Elway being hormonal and desperate. However, it is possible that Elway is angling for a major coaching hire. Maybe he'll make a push for Urban Meyer. Mike Shanahan would be an intriguing possibility, He was Elway's coach when he won the SB and Elway was not the GM when Shanahan was fired.