How would you make that argument? It seems tricky given that D&D-style Paladin is now a fairly common non-literary fantasy trope, but in most fantasy there isn't a strict association between LG/Code and Paladin powers - the powers seem to remain (sometimes become dark mirrors of them, of course) even when the Paladin is less than virtuous, and some Paladins have powers whilst being complete jerks.
Preference isn't really argument, though. You've not shown why you think it's "essential". Given the archetype can clearly work without those (hell, right back to the Solamnic Knights we saw that), it seems a hard one to make.
It's simple. D&D tapped into the meaning of paladin as a knightly champion. The knightly implies chivalric which would include tenets like:
Believe the Church's teachings and observe all the Church's directions.
Defend the Church.
Respect and defend all weaknesses.
Love your country.
Show no mercy to the Infidel. Do not hesitate to make war with them.
Perform all your feudal duties as long as they do not conflict with the laws of God.
Never lie or go back on one's word.
Be generous to everyone.
Always and everywhere be right and good against evil and injustice. [borrowed shamelessly from wikipedia]
Right there, we're pretty much ruling out anything but good. Consider the strictness of the external code and I'd say we're also talking lawful because there's little freedom for individual interpretation or choosing which tenets to follow. The additional restrictions imposed in D&D dating way back to the original Greyhawk supplement serve to increase the strictness load even further. And through his devotion, he has some potent divine grace.
The paladin adapted not simply a religious warrior - it adapted a specific sort of religious warrior - one based on stories of Christian knights and other heroic ideals. Tempus Thales of the Sanctuary anthology may be a religious warrior with his own powers (including regeneration) and restrictions (must not take a woman in any gentle manner) but there's no mistaking him for a paladin by any common conception of the term. It needs more than "religious warrior". The paladin as conceived in the Greyhawk supplement and running through 3e was a much closer mapping to the term paladin because of his codes and alignment than 4e or, as we're learning, 5e. A paladin that could be devoted to any god, particularly an evil one, really doesn't fit the term.
One of the most ironically humorous aspects of D&D's history has been the disapproval of certain Christian authorities and groups when there are no fewer than two character classes significantly influenced by Christian mythologies, one of them being the morally upstanding and strict paladin - the exemplar of the knight in shining armor and heroic (and here I don't mean Greek heroic) archetype.