One major problem is that "interoperability" has too many interpretations. It is often substituted for the more relevant term "intraoperability." The first word actually originated from the Information Technology field, where it refers to the ability to read databases created with multiple programs via single platform. As many of us know, sometimes IT and radio communications concepts don't mix well. (That is why the IT department should not be placed in charge of the radio system. But I digress...)
Ability for units within the same agency to communicate = operability. Basically, whether or not the local radios work. Local fire departments in my area seek to ensure this by the daily radio check ritual that I refer to as "counting the fire trucks."
Ability for units from other agencies within the same service and geopolitical zone to communicate = intraservice intrasystem operability. This is managed by having a countywide or regional system that is shared by agencies in the designated area. Local mutual aid channels/talkgroups should be designated.
Ability for agencies from different services within the same geopolitical zone to communicate = interservice intrasystem operability. It should not have to be managed on a nationwide basis. That is how we get the kind of screwups that can occur if NIFOG is applied locally (like the .340 issue). Local interservice channels/talkgroups should be designated.
Ability for agencies from other geopolitical zones to communicate = intersystem operability. In this situation, the agencies' "home" radio systems are not the same. If they are within the same frequency range (good) and based on the same technology (better), then interoperability is not a problem. This is where NIFOG begins to have some applicability because different groups of users need to share the same frequencies and tech for mutual aid purposes and radio communications are regulated at the federal level.
Frequencies are one thing and protocols (emission modes, modulation techniques, etc.) are another. Unfortunately, where the feds have made actual enforceable rules about frequency selection, they have utterly failed to make enforceable rules about protocols. Even when they try, too many back doors are left open and the language is so vague as to be open to local interpretation. The telecom industry defines what the buzzwords are supposed to mean according to their needs (compatibility, interoperability, privacy, etc. are all defined by advertising copy), and Congress, the FCC, and other regulatory bodies dance to their tune.
All of this is a lengthy way of agreeing with SteveC's comment above and providing some rationale for it.
Of course, I have only addressed the technological side of the problem. The human problem cannot be solved through technological advances. People still have to play nicely together regardless of where they are from or what uniform they wear. So far, we don't have a universal solution for that.