Feels nice to be able to know who's who again.
That seems to be the case in both old and nu canons. The Grand Clone Army seem to be the "elite" despite that they have such pathetically low numbers while regular civilians instead sign up for the Sector Armies which are responsible for protecting different sectors within Republic Space, with the total number of soldiers numbering in the billions.
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But as you pointed out, the people of the Republic aren't exactly competent or used to war of such a scale, as seen with the Naboo Army, the Auril Armies, the Savareen Armies and those shitty "rebels" from Onderon. Probably because they were so lazy and complacent thanks to the modern lifestyles and peaceful times before the Clone Wars.
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So the Clones serve as a good backup, elites, and excellent powerhouse units alongside jedi generals.
Even the Separatists had organic armies in their ranks, but unlike with the Republic, the droids far outnumbered them.
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From what I understand, back when Zahn first started writing the Thrawn trilogy, he went around asking and looking up any source he could to make sure he got the setting right. This included asking the writers of the SW RPG, looking into comics and even asking George himself about the timeline of events and the Clone Wars. From what was George's canon at the time (which was constantly prone to internal changes) the Clone Wars and the rule of the Empire lasted for far longer than what the prequels implied and it was apparently a war between clones headed by the "Clone Masters" which I guess George later developed into the Kaminoans who went from being evil masterminds to a 3rd party business manufacturing clones for other masterminds.
Despite this change, some Dark Horse comics tried to bring back that element by making it so the Separatists made their own elite clone army, but after a lengthy war their production was sabotaged and halted before they could even leave the planet they were being created on.
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Like with Republic clones, these guys were made from a legendary assassin but who was not human.
The OG Battlefront II also brought back "Clone Masters" as rogue Kaminoans trying to create their own army to fight back the Empire, but they too were defeated in the end. This resulted in Palpatine subjugating the Kaminoans and shutting down all their factories while outlawing cloning (unless directly overseen by himself) and focusing on traditional recruiting. And then there's Atha Prime who I've spoken about before in regards to sequel shit if anyone remembers. The end result is that there were CIS and others who tried to use clones to fight the Republic/Empire, but they ended up losing. I still would've preferred the original interpretation from the pre-prequel stuff of clones being the bad guy army since it would've made more sense and that its basically slavery anyway.