According to the EU, the Republic was so vast and powerful few had the power to argue with it. That might be why they had no standing army. Strangely enough, even after AOTC, it never occured to me to think that the stormtroopers are clones. It wasn't until some tectless jerk on another forum argued with me that the though occured. After all, the Clone Wars had pasted twenty years. Cloning wasn't common in the EU. That gave the impression that after the Clone War, cloning wasn't necessary or the technology lost. After the establishment of the empire, raising troops shouldn't be a problem. I would think that even civilians fought in the Clone War. After all, how ridiculous is the idea that in the entire galaxy no one wanted to fight for the Republic/Empire? While I might agree that essentially having an army of mindless slaves would add to the evil of the Empire, it just sounds ludicrous. One person suggested that the Imperial Academies were only for officers. Why train recruits as officers when one could raise a specialized clone?
One complaint I have with the prequels is just how bloodless the wars have been. An army of Droids against an army of mindless, ever loyal clones just kind of removes the idea of a galaxy at war. The OT had a divided galaxy. The Empire had its supporters, while others fought in the Rebellion. You had the concept of brother against brother in a galactic civil war. In the PT, you basically have a select few playing a game of galactic chess with seemingly little at stake. If you saw a rebel killed in action, one could think, "There went someone father/brother/etc". In the PT, it's, "Looks like we need to build more droids" of, "We'll grow a new one". Sure, there are the worlds that are ravaged, but I still think it really takes something out of it. It's like the rest of the galaxy couldn't care less so let the Republic have it's little war. That's the image presented in prequels. I too agree that the Jedi seemed to accept the clone army without question did seem a tad odd. I alway assumed the clones were going to be the enemy. Why else call it the Clone War? This seems more like the war of the Sepertists.
Most likely, when Lucas wrote the words "You fought in the Clone Wars?" he was merely thinking up something vague that sounded interesting. With little thought to anything else.