I have a feeling that we've had this conversation before - but my experience on this is 100% the opposite.Because, and this is strictly IMO, that archetype just doesn't work without the LG-only restriction.
Sure, you can play a heroic warrior archetype without the restriction if you want... but in practice, the very instant the Paladin's code becomes an inconvenience the player will suddenly decide that it's just not worth the effort. The code has to have mechanical backing, or it is meaningless.
I have never experience satisfactory play of priests or paladins in a "strong alignment" environment - because the game degenerates into one of "second guess the GM".
Whereas in alignment-free environments I have seen repeated instances of top notch priest and paladin play from a range of players. The key, in my experience, is to set up a situation in which the stakes matter to the player.
Just one example: Not too many sessions ago, the fighter-priest in my game found himself obliged to insist that a prisoner the PCs had captured by imprisoned rather than executed - despite knowing that, as a priestess of Torog (the god of jailers) she would probably enjoy herself in prison and soon find her freedom. This came about because (i) the other PCs tricked her into handing over information in return for a promise, on the absent warrior-priest's behalf, that she would be spared in return, and (ii) the warrior-priest came into the interrogation room, and was therefore informed by the prisoner of the promise that had been made, before the other PCs could execute her in disregard of the promise by which they did not feel bound. (The lead interrogating PC was also pissed off, because having been more-or-less deputised to lead a successful interrogation, his best efforts were thwarted when the "paladin" came back into the room and therefore undid the good work of the interrogator's skillful duplicity.)
Now we do not use mechanical alignment (it's a 4e game). There is no mechanical stake in the PC breaking his word, whether given by him or by his companions on his behalf. And there is no denying it would have been more expedient for the PCs to have executed the prisoner in any event. But the player wants to play a certain sort of PC - an honourable warpriest of Moradin - and the whole situation in the game is set up around the PC having that persona (he is the party's leader, for example, when dealing with external political and social actors). It is part of the story of the PC, and the player doesn't want to derail it. It's not part of the PC's story - as conceived of and developed by the player - that he be an expedient breaker of promises given in his name.
Convesely, if the game is set up so that only expedience matters, then naturally players will be expedient. But that is already a game in which the paladin archetype makes no sense, and you can't change that around just by turning up the alignment dial.