This is probably the reasoning they had at the time, but in fact (as demonstrated later by actual combat) the sabre was still the superior weapon for mounted action and in fact was able to defeat not only dismounted enemy dragoons but all-up entrenched infantry on occasion.
It's not the ideal weapon for all circumstances, not by any means, but it's the best weapon for some common circumstances.
I don't think of a saber as a great weapon in the CW era. Any kind of ranged weapon is going to outdo the usefulness of a melee one. Like in Three Month in the Southern States, Fremantle mentions that Confederate officers spoke of the shotgun as the best weapon for mounted use, I'd have to concur. In a close cavalry fight one shot will take out more than one enemy soldier, and you had two.
Plus I seem to remember reading in several books that George Washington spoke of the blunderbuss, a shotgun-type weapon itself as a grand cavalry arm. In the American scheme of things cavalry wise, sabers have never been popular, neither have big epic European-style cavalry tactics, we've always done our own thing which is why North & South hearing of their actual use is memorable day.
Also its kind of out there to speak of cavalry in the CW era able to defeat everything up to entrenched infantry. As a general rule, cavalry on both sides tended to avoid clashes with infantry, only doing so when they had the close support of their own infantry. Cavalry and their sabers were pretty much obsolete in the Napoleonic sense, and to do anything like in Napoleon's day would have been a guarenteed slaughter because of the advances in weapons, and they knew it.