And if they have horses why are they infantry and not cavalry
Because they’re not trained to fight on the horses, and the horses may not be combat-trained either. Infantry throughout history has often used horses or mules for transport, then gotten off them for the actual fighting.
To add to the list of criticisms: They knew what route they would be retreating along, so why were there no traps? Even if digging a concealed pit would have taken too long, a few chevaux de frise, tactically placed, could have done some damage. Or give the rearguard some caltrops to toss behind them. Horse archers could have helped a lot, but would probably have been too much to ask for.
I get the impression that the person responsible for the source material for this series doesn’t have even my passing interest in the nuts and bolts of medieval warfare.
Dragoons were a more recent incarnation. I believe there were other earlier ones.
Basically what went wrong with this scene in Reincarnated Aristocrat, though, is that they went for too much detail in a crowd scene that would have been much better off with less. If you look at older anime from the hand-drawn cell era, they didn’t try to individually animate every member of a large group like an army. Exaggerated atmosperic perspective and depth of field, plus judicious use of detail, reduced the parts of the army away from the main characters to a sort of dark mass with the occasional helmet or horse-leg movement—and that was okay, because we didn’t care enough about those people to focus on them individually. Currently there’s a fad for using computer animation to spam copies of the same model, often poorly animated, to make up the numbers, and it doesn’t work and tends to be very noticeable. Hopefully someone in Japan will eventually figure that out, and they’ll return to the more painterly approach.
(In this case, of course, they didn’t even spam enough copies, so even worse.)