The concept

With the vanishing of alignment restrictions on Paladins in 5e, I have been toying with the idea of a (PC or NPC) Lawful Evil Paladin.

My particular image is of a Noble background Paladin with:

• Personality Trait: If you do me an injury, I will crush you, ruin your name, and salt your fields.
• Ideal: Responsibility. It is my duty to respect the authority of those above me, just as those below me must respect mine. (Lawful)
• Bond: My loyalty to my sovereign is unwavering.
• Flaw: In fact, the world does revolve around me.

He has a firm and unshakable belief that society as currently structure (i.e. with him near the top) is the way things should be; anyone who seeks to challenge or change this is, by definition, evil in intent if not in deed.

The Rules

Relevantly, the rules have this to say on Paladins (PHB pp. 82-88)

paladins are united by their oaths to stand against the forces of evil.

A paladin swears to uphold justice and righteousness, to stand with the good things of the world against the encroaching darkness, and to hunt the forces of evil wherever they lurk.

are you an embittered loner sworn to take vengeance on those who have done great evil, sent as an angel of death by the gods or driven by your need for revenge?

did some terrible event—the destruction of your home, perhaps—drive you to your quests?

paladins are rarely of any evil alignment

The tenets of the Oath of Vengeance vary by paladin, but all the tenets revolve around punishing wrongdoers by any means necessary. Paladins who uphold these tenets are willing to sacrifice even their own righteousness to mete out justice upon those who do evil, so the paladins are often neutral or lawful neutral in alignment. The core principles of the tenets are brutally simple.

Fight the Greater Evil. Faced with a choice of fighting my sworn foes or combating a lesser evil. I choose the greater evil.

No Mercy for the Wicked. Ordinary foes might win my mercy, but my sworn enemies do not.

By Any Means Necessary. My qualms can’t get in the way of exterminating my foes.

Restitution. If my foes wreak ruin on the world, it is because I failed to stop them. I must help those harmed by their misdeeds.

I have highlighted the really key bit – paladins are rarely of any evil alignment – which means that there are some paladins who are. I have also focused on the Oath of Vengeance paladins since the tenets of the others are more directly in conflict with an evil alignment.

Relevantly, the rules have this to say about alignment (PHB p. 122)

Lawful evil (LE) creatures methodically take what they want, within the limits of a code of tradition, loyalty, or order. Devils, blue dragons, and hobgoblins are lawful evil.

So, apart from 35+ years of tradition, is there anything in the 5e rules which makes this unworkable?