[Morthoron]

Marky does have a point in regards to how the outcome of battles were predicated on the presence of personal leadership, even in wars up to the 15th century (rl history). The "cult of personality" was a very strong motivator, and the defection, death or capture of well-known warriors or princes could have a deleterious psychological effect on battle.

Therefore, with the sudden absence of Gandalf (who had in effect saved the scattered forces of Erkenbrand) in Gondor, and then the sudden departure of Aragorn and his grim Dunedain (who made the Rohirrim look like boys), along with mythical figures (to the Rohirrim anyway) such as the Elf Legolas and the Dwarf Gimli, it could have a decidedly negative effect on the Rohirrim. Tolkien didn't consider the implications most likely, and preferred to ignore this avenue of the plot.