This sort of objection to paladinhood is like criticising the X-Men because instead of doing useful things, like (say) using eye-blasts to drill bores, and using weather-control to alleviate famine, they waste their time fighting Arcade and Dr Doom. What that criticism really is is a rejection of the genre (qv Watchmen).
No, it isn't. Because Dr. Doom is actively trying to harm people. Stopping the man who wants to harm people is good. Also doing common sense out-reach to make people's lives better when you are constantly fighting a PR campaign of how people hate you for being too dangerous is ALSO a smart thing to do, but we don't but we don't refuse to fight evil just because making plows will stop starvation.
A paladin only makes sense within a providential conception of the world - where personal honour is part of what is demanded/expected of human beings as part of the divine plan. When, in Excalibur, Arthur proclaims that no knight who is false can win, in single combat, against a knight who is true he is not making a prediction about prowess: he is affirming his faith in the workings of providence.
In the context of FRPGing, a lot of this is up to the GM, insofar as the GM controls consequences. If the GM frames consequences in such a way that knights who are true lose, rather than prevail - or cause a lot of harm to innocents as a result of their fighting - then the GM is presenting a world in which paladins have no place. That's fine if that's what you want - there's no room for paladins in the world of REH's Conan - but I think it helps to be clear about what's going on.
So... you realize with this you have effectively given the Paladin premier place in the fiction, right? Because by Arthur's assertion, a rogue who fights via trickery and deceit would always lose to someone who uses no trickery or deceit. The wizard who uses magic would always lose to the "true knight" represented by the paladin.
And so if the story is to present that the rogue or the wizard can be heroes whose methods cause good... then the paladin no longer has a place in the game, according to this theory. Which means the person who wants to play a paladin (or the DM who decides this) now gets to dictate everyone else's character and their arc. They all MUST affirm their faith in the workings of Providence, or lose. They cannot find strength in other callings, or approach a problem in different ways.
But, as a counter point, I never said that Paladins couldn't be in the game. I said that the paladin who refuses to sneak, and instead charges the front doors of the keep, is putting their pride in their nobility and honor, before the good of the people.
Consider this. A Devotion Paladin takes an Oath to never lie. They are grabbed by the BBEG, who demands to know where the Orb of Ultimate Power is located. Now, a rogue, might lie, might deceive the dragon and save their own life. The Paladin who says "I cannot tell a lie, the Orb of Ultimate Power is hidden in the Village of Hex" may feel like they are being noble, not deceiving and being honest in all ways.... they are also being an IDIOT. Because "I refuse to tell you" is ALSO not a lie, but hides the Orb. But I have completely seen people do this. They have acted against the interest of the party, against the interest of the innocents, all to make sure everyone is aware that they are Capitol G Good and have never used an underhanded tactic ever. They won't even lie by omission!
This isn't to say the paladin has no place in the game, because I have seen highly honorable, highly courageous, exemplar characters who are Paragons of Good... trick people. They don't lie, they just don't correct your assumptions. They teach humility by being humble, they teach honesty by being honest in ways that matter, not to show off but in ways that a nobleman (who many of the chivalric ideals were based around the ideal nobleman) wouldn't do. And these characters show case to me that it is possible to be honorable and good, meanwhile, characters who are loud and blatant about "I shall never do anything to dishonor my highly honorable honor because I am honorable and will not act dishonorably!"... seem to forget the point is to be good. Being a good person takes second chair behind Honor, Nobility, and being seen being Honorable and Noble!
Which I think goes against the spirit of the class. Just like a hero who is more concerned with a "fair fight" isn't much of a hero when they care more about being fair, than the safety of the citizens who are in danger.