Coughlin is A problem; he might not be THE problem. His horrific coaching staff and loyalty to over the hill players and coaches is his undoing. Also, you can't realistically say, "well, we fired the OC, DC, and then another OC in the past three years and the results are not satisfactory, but none of that is Tom's fault." He's in charge of those hires, plus the buck stops with him; it's at least partially his fault.
That being said, this roster is awful. Nobody could be successful with this team. When we're ecstatic about finally getting a linebacking corp that consists of JT Thomas, Jasper Brinkley, and sometimes Devon Kennard, you're in some trouble.