I don't know about that. Coruscant by itself could have as many volunteers as your average Republic planet has people. The Republic is pretty big so they should be able to get trillions or quadrillions of volunteers needed to fight the septillions of battle droids.
But I always assumed the reason the clones were necessary was because the Republic was full of decadent and otherwise lazy people who wouldn't want to join the military and trying to conscript people would cause mass riots and defection to the CIS. The Republic's military was also pretty shit before the Clone Wars, like remember the guys at the start of The Phantom Menace? Yeah, that's the Republic's military, it's an underfunded police force with shitty starships and probably no greater training than being able to say OY MATE YA GOT A LOICENSE FOR DAT.
There were tons of advantages to running an army of clones, of political, economical and military nature.
Politically, the GAR was an army of slaves. They had no political representation, i.e. nobody can make a fuss about casualty rates or poor treatment. The Clones couldn't do anything but obey and play along, which is what they were specifically bred for anyway, they didn't even have basic human rights, let alone a lobby. Most people viewed them as not much more than living droids.
They weren't paid, neither did the Republic have to pay compensations in case of injury, death, marriage, vacation, childbirth, bonus for going to war etc, no retirement funds, no support to re-enter civilian life. Lots of that funny stuff that makes a soldier stupidly expensive suddenly just isn't a problem anymore. Thinking a step further, the Republic is in total control of the narrative by using a clone army with no representation. The war is that weird thing the news anchor talks about, it has no measurable effect on the population, there is barely any ground for dissent to take roots. No letters from the front about how terrible this war is, no parents mourning their children. All you'd get is perhaps more jobs to help the war effort. If the war reaches a planet, the population can be instrumentalized to demonize the CIS.
Then we look at the Clones' commanders, the Jedi. The Jedi have in ancient times sworn to defend the Republic at all costs and will put up with any hardship to see their oaths fulfilled. They were effectively guilt-tripped into the war by their moral code and history, with the Council even giving the ultimatum "either you fight or you can fuck right off and leave the order." They're dogmatic, oath-bound warriors who didn't dare to speak up because they'd see it as morally wrong. Incidents like Barriss can just be swept under the rug, conscientious objectors can be easily deplatformed.
The elephant in the room here is that the Republic hasn't been at war for 1000 years and had no standing army to be suddenly put into action. All you had was local planetary armies effectively playing dress-up, with varying levels of loyalty, gear and training, doing at best low-intensity counterinsurgency against pirate groups or something.
You usually can't just go and conjure up an army out of nothing, you can't just get an army ready for a single conflict, you need to keep it up permanently to be ready in case something goes awry. Now imagine the cost of a standing army that does nothing for 1000 years only to be called to action for a period of maybe 20 years (The GAR was raised after the Naboo Crisis, fought in the Clone Wars and early Imperial campaigns) to an army that was specifically bred and equipped for this period with the most advanced technology and then could just be dumped once they were no longer needed.
What we're looking at here is a galaxy-spanning, highly advanced economy capable of unprecedented output and R&D at an extreme pace, with people who are the undisputed masters of Cloning spearheading the effort. This wasn't sorcery for the Kaminoans, it was essentially Tuesday, except on a slightly bigger scale. The Republic already had the facilities, dockyards, industrial hubs, what have you. Even with factoring in R&D for equipment and training regimens, the GAR would be extremely cheap in comparison to training and sustaining a standing volunteer/conscript army of similar size, let alone capability.
Dooku hosted what effectively a tournament to find the most fitting genetic template for the Clones. With our winner Jango Fett, we have a template with decades of bounty hunting under his belt, a survival artist, an experienced fighter pilot and capable of killing even a Jedi. Now we change his genetic code just enough to turn him from a rugged lone wolf killer into a loyal and obedient soldier, adapt it to what we specifically want him to do and throw in some extra goodies like faster aging so our guys can go and fight sooner, unquestioning loyalty, extreme resistance to stress etc.
Think of the crazy stories of soldiers from history, guys like White Death, John Basilone, Carlos Hathcock, Erich Hartmann, Kurt Knispel, what have you. Now you have a full army of only these guys, the absolute apex of human soldiership. The Clones are simply the best human soldiers you could imagine. Any other army would look like a LARP group next to these guys, which is why volunteers were so uncommon in the GAR.
They just don't compare, have actual human rights, negatively affect the home front and cost way more money on top of that. Fuck that.
