@exlibra i figured i'd pull this out into a full rb since... well, there's a lot here.
so! debate and speeches! first and foremost (as you probably already know) oratory is a huge cultural touchstone in ancient rome. it's an important component in the education of citizen boys; proper knowledge of oratory is essential to participate in public life, and lacking proper rhetorical skill can be a huge social stumbling block (see petr. satyrica 2).
we can see how this mentality is relevant to cardassians as well, both due to how essential argument is in their day-to-day social interactions and the way that verbal competition is involved in their social hierarchy; recall jellico's mention of cardassians' "instinctive need to establish a dominant position in any social gathering" in tng's chain of command.
your accurate observation (that a love for public speech and argument seems on its face somewhat awkward to combine with cardassians' need for social conformity) can be applied to rome as well. starting under augustus, there's nearly as clear a picture as there is on cardassia of what a good roman vir should be.
what i think the answer is here is that cardassia, like rome, was a republic before it was an empire. rhetoric is, of course, an absolutely essential skill to the political machine in a society governed by a senate. i imagine that life under the cardassian first republic, before the military takeover, might have been similar: much like rome, the need for eloquent political maneuvering would exist on the governmental scale and, as a result, gain an extreme cultural importance.
steven h. rutlidge's "oratory and politics in the empire" in a companion to roman rhetoric has some interesting insights into what happened to this senatorial rhetoric once the empire was established:
under the emperor, the specific kind of political debate ceases to have as much relevance, but that doesn't mean its importance to roman society evaporates overnight, and it ends up maintaining significance despite the fact that it must now operate in a more precarious context (you can't exactly run around delivering invectives against the emperor).
now how do you navigate these "restraints and limits"? roger rees has a good chapter on panegyric (praise-centered oratory) in the same book that i'm going to use as an example. first, because he opens the chapter like this:
which feels rather relevant to the way non-cardassians tend to view their practice of social maneuvering and obfuscation. second, though, since i'm (unfortunately) an avid cicero fan, he's always on my mind when i'm thinking about rhetoric, and rees has this to say on cicero's use of panygeric:
this is what i was getting at when i mentioned criticism of the cardassian state between the lines. warm, open praise of the empire is something we catch a lot from garak (and from other cardassians). concealing criticism within open speeches of praise is a perfect way of reconciling a culture's foundation on eloquent speech with the realities of what it means to live under imperial rule.
i mentioned poetry, as well, thinking about how ovid famously says that he was exiled from rome because of "carmen et error," "a poem and a mistake" (tristia 2.207), and how i always remember this phrase when i hear any mention of iloja of prim's vulcan exile. prim lived during the first republic, and could have, much like ovid, seen its end. the sort of poetic tightrope-walking that we can find in a lot of roman poetry, where criticism of the empire is shrouded in praise (ovid's met. and virgil's aeneid are two of the most commonly analyzed this way), feels really cardassian, and it therefore feels likely to me that iloja may have been exiled due to a carmen et error of his own.