Working through your circular arguments, first you proclaim:

"Anyone thought about the Lebanese and Palestinians who are violently opposed to Hamas and Hezbollah?"

So I suggest that by recoginizing these groups as part of the state they would more likely be held to task by such others. But then, you come back with:

"but that is not true. Very large and significant portions of the populations do condone their actions"

To which I would add "of course, all the more reason to recognize that these organizations speak for the state and that the state should be held accountable as well as the organizations for their actions."

We grant these groups sanctuary. Not just these two groups, in these two states; but ALL such groups in whatever states they emerge from. The information age (that yes, I realize you are equally dismissive of), or more importantly the knowledge age, that is fueled by the greater speed and availability of information is empowering populaces and non-state organizations in new ways. States are the last to recognize and adjust to this; as usual it is the previously disempowered (people as individuals and as organizations) that embrace the new tools first; and the ones who have power who resist it most as applied against them.

Either way you slice it, be it that these groups don't or do speak and act for the people of the state; the fact remains that they are more easily deterred from acting badly when allowed to operate within the system, and also held to task by the system. Outside the system they enjoy a tremendous sanctuary that I suspect we don't appreciate because so many still believe the simplistic cliche' that "sanctuary comes from ungoverned spaces."

Yet one more example of Fairy Tale-based COIN doctrine (the first being the Pied Piper theory of ideology, that well governed populaces will become radicalized by some seductive ideology and follow the espouser of the same to their doom.)

This one is "The Sherwood Forest theory of Sanctuary." Everyone knows how Robin Hood and his Merry Band took sanctuary in Sherwood Forest; but if the forest was destroyed or somehow denied to them, would they have no more sanctuary?? Of course not, there are other forests for what a forest provides; but more importantly the true sanctuary came from the support of a poorly governed populace (the illegitimacy and injustice of Prince John is legend as well), and their outlaw status itself. Sanctuary comes from such popular support and legal status (a sovereign border, a lack of state affiliation, an outlaw status). As an aside, we approach the AF-Pak problem like a mob of woodcutters going after Sherwood Forest. Even if you cut it down, you have only forced a change of address if you have not addressed the primary sources of sanctuary.

We need to move past fairy tale COIN and get real. We need to get real with groups like Hamas and Hezbollah and the states they live in as well.