In medieval and antique Europe, royalty and nobility in general was often expected to fight on the battlefield. It was only in early modern times when gunpowder and pike squares started making heavily armored knights and especially heavy cavalry obsolete that this fundamentally changed. That said, LotR is indeed rather idealized, and it definitely follows ancient tropes of beings who are better than humans in every way and yet can and will breed with humans occasionally (thus Aragorn and Elrond).