For one thing, the French army were not in the least amateurs. Conscript does not mean amateur. These were the battle-hardened victors of Marengo, Ulm, and Austerlitz. They would go on to be the victors of Jena, Auerstadt, and Wagram. The Prussian army was a typical 18th century barrack slave army of sullen lifers led by the lash, the noose, and the gauntlet, essentially a marching maximum security prison that would desert at the first opportunity, fighting for fear of their officers instead of patriotism. The French Army was flexible and motivated and ability was rewarded with promotion, whatever your social origin. The Prussian Army of Jena was rigid and reactionary.
The purpose of creating a public education system was the desire of Scharnhorst and Gneisenau to change Prussia from a barracks of cowed slaves to a patriotic nation. The stark contrast between the servility of the Prussian populace to their French conquerors and Spanish people's war shamed them. To create an army motivated by patriotism instead of terror. It was not about absolute obedience at all.
For instance, what made Napoleonic victories so much more decisive than Frederick's was the concept of pursuit. It is pursuit that prevents a defeated army from regrouping and fighting again another day. It is pursuit that turns a defeated army into a mob of refugees. Frederick could never pursue because he could not trust his men not to desert if they were ever beyond the strictest command control. He could not trust small units to engage the enemy on their own initiative. Napoleon could trust the patriotism and initiative of his men. The Prussian reformers understood that to copy French tactics you had to have a people's army, not a barrack slave army.
"Don't be a cowed slave - go to a government school. Or we will throw you in jail. Besides, you know you are to stupid to educate your own child."
Sounds like they just wanted obedient cowed slaves.
What do a couple of pocket battleships know about education, anyway?