To begin with, Iconoclasm is an era that is completely shrouded in mystery and lack of information. Most of our historians (including my current Arch-Nemesis Theophanes) were expressly iconodules and as such were not fans of Iconoclasm and usually had a bone to pick with Constantine V for really being "the guy" when it came to iconoclasm. Almost everything is conjecture since our historians are incredibly incredibly incredibly (did I say incredibly?) biased against the Iconoclasm regimes. To my knowledge, there's very little evidence of Leo III doing much more than ordering that Icons be taken down from the focal point of the church (the famous story of his removing the icon from the Chalke is likely bunk, there's more evidence to show that he simply put a cross where there was nothing to begin with since the Cross was often the symbol of the military). My theory, and one shared by many, is that Leo III was slandered by Theophanes as a way to further discredit the hated Constantine V by making his father illegitimate.

The idea that, at least I got from Leslie's book, is that Iconoclasm was very much a response to the Arab raids devastating the Anatolian heartland. The Roman consciousness was one of superiority and everyone else being barbarians along with being God's chosen people, so how on earth could they have been getting the snot kicked out of them over and over again? The answer to people out in the countryside was idolatry. The caliphate, being muslim, had a fairly strict prohibition on the use of images in worship as a way to avoid idolatry, and this was well known to many in the country side in part due to the fact that the caliphate stopped using Byzantine coins once the face of Jesus was put on the Byzantine coins and coins from the caliphate were coming in with just lettering. When you are being destroyed, you want to find an answer, and according to this argument the answer was that the Muslims were being rewarded for their getting rid of idolatrous practice. This is why we have evidence (for example, letters from provincial priests and bishops) of the countryside being fairly iconoclastic while the capital remained fairly iconodule, they had nothing to worry about.

Likewise, Iconoclasm served as a way to reassert central authority. The Empire's government apparatus had half-way broken down following the devastation of the Arab raids and especially the upheaval of the post-Heraclian chaos, and so it was often the local monks and holymen who were looked to for guidance instead of the provincial magistrates. Constantine V, in his characteristic centralization paradigm, could therefore establish a strict central idea of what worship had to be like and use it to impose imperial control where it had been slipping. Constantine V established his idea of orthodoxy and could use it to cut out those who weren't in the imperial camp. It wasn't the holy man in the mountains that could help you, it was your local friendly imperially approved priest that you needed to go to for guidance. It's also likely that Leo III's "iconoclasm" was much more in response to the extreme devotion that icons were beginning to get (there's little mention of Icon devotion until the Arabs arrive).

Source: Byzantium in the Iconoclast Era, c. 680-850: A History

An (in my opinion) amazing and incredibly accessible overview of Iconoclasm is the History of Byzantium Podcast. Robin in no way simply follows the chroniclers and does a lot to try and give the latest and most modern understanding of what the period was.

There is a lot of debate to how much iconoclasm actually "tore" at society. There is a fair amount of evidence that the violent, cultural revolution style, smashing of icons was greatly exaggerated to suit the successors, who "restored" God's favor by ending iconoclasm.

We do now that during Leo III's reign, an icon above the Chalke gate was removed and there was some (or possibly a lot) uproar about it. A telling thing is...it was not smashed. Later, it was reinstalled. Some theories say that it was only taken down for renovation. Leo tried to shift blame from himself, partially using icons, but the fact is there is little evidence that many icons were destroyed. There was a shift in how murals were painted at the time...they shifted to similar, non-person images like the cross (the Christ icon from the Chalke gate was itself temporarily replaced by a simple cross) but for the most part, especially for the common folk, icons remained a part of the culture.

More to your question. There is a good chance later rulers like Irene used iconoclasm as a scapegoat to why the Romans could not stand up to the Arab invaders. Thus by "restoring" tradition, they were "restoring" the grace of God. The whole thing was probably more the abstract theological debate you would think it would be.