Howie and Kevin -
The Russian examples I have seen in 1805-7 period are typically conducted in blocks of 10 squadrons - the charge of the Constantine Uhlans at Austerlitz is an example, and the later charge/countercharge of several bodies, either individual light cavalry regiments or pairs of heavy cavalry regiments, but typically around 10 squadrons. There was a larger mass or Russian cavalry charging Augereau at Eylau, but my perception is that this was not a very well coordinated charge, though it did the trick. The French were the only army to actually train coordination of larger bodies of cavalry as far as I know, and if you don't practice a maneuver, it's risky to try it for the first time on the battlefield which helps to explain the "why" question.
But the other element is one of understanding what is actually being said. When the Russians charge in bodies no larger than a regiment, they are charging in bodies of no more than 10 squadrons, or in other words something between the typical French light cavalry brigade of 9 squadrons or a division of 12 squadrons. the Austrians often distributed individual cavalry divisions (the two-squadron division, not the larger multi-regiment division), but there are examples of full regiments operating as a unit and charging together - here 8 squadrons or again something like a French cavalry brigade. So stating that the allies never charged in anything larger than a regiment is a bit misleading, as the parallel body of cavalry on the French side would be a brigade. when the allies fragment their regiments and "scatter" them by detaching a division, this is not really any different from the French detaching a regiment for scouting/observation (2 squadrons vs. 3).
The larger French mass cavalry charges are really the exception, the norm being smaller bodies (9-18 squadrons from the examples I've studied). The implications of the difference in size of cavalry regiments, though, is that the French are really forced to develop coordination among regiments in order to achieve the critical mass required by the more typical charge (and there are many examples of French charges involving 3-4 regiments) while for the other powers this more typical operational body involved only a single regiment (two at most) and therefore didn't require the same level of coordination between regiments.
Realizing this, though, highlights the advantage in command and control afforded by the smaller regiments, namely a higher ratio of officers/squadron. This also reveals a connection - the French develop inter-regimental coordination to operate at the "typical" level of 9-12 squadrons, which lends itself to grouping more regiments together and actually provides the framework for the large-scale cavalry charges. By contrast, the allies lack the conceptual framework for regimental coordination (which isn't needed for the "typical" cavalry operations in smaller armies) which makes it difficult to coordinate larger bodies of cavalry.
Does that make sense?