I think you've sparked a good question, by "why not" in other armies? In my own opinion it goes to the question of command-in-control and the democratic tradition of the French revolutionary army. Reading both contemporary accounts and professional (military) analysis of Prussian chain of command (and similarly Russian) the gulf between officer and enlisted was enormous.
If you read Parquin or other French accounts of cavalry the distinction between officer/enlisted is hazy, and it is as if when the colonel gave a command, the squadron/company leaders knew instantaneously the objective and the method. I don't see this is Nadezhda Durova's accounts of the (Russian) Polish Uhlans or Maripoul Hussars. The officer/enlisted relationship is strained and distant, with officers often riding off abandoning their men and never having a clear understanding of what the Colonel wanted. While Parquin (even as a subordinate enlisted) knew and had strong feelings and respect for his Colonels...Durova often doesn't even know (or had even seen) her Colonels, who were aloof and distant.
Take these inter-regimental problems in command-in-control and move them up the chain of command, and I think you see why a multiple regiment charge within the Prussian or Russian army were difficult if not impossible. As someone said before, true organization above the level of regiment was "ad hoc" in most European armies in the early Napoleonic wars.