I don't see alignment so restricting. In my gaming circle at least, alignment is just a guideline for the players (or a ref playing an NPC) on how to express the character. There is no cop, not even the DM, coming down hard if the player "violates" alignment.
If you are chaotic good, you don't care much for the rules of others but you are going to pay some attention to the well being of others when making your decisions. If you regularly do otherwise, you might get called out by players or the ref but no more so than if you said your PC had a dreadful fear of water and then kept forgetting that fear when making your decisions.
As long as you make a reasonable and reasonably consistent attempt to interprete your alignment, we're all good with it.
The case of the paladin mentioned by the OP is a perfect case in point. It doesn't take much reading of history to find many knights who felt they were paladin-esque and likely would have considered themselves lawful good. They span a wide range of personalities from folks more intune with modern sensisbilities to some fairly horrendous people (at least in how they could act in certain circumstances such as against non-knights, infidels, etc.). Yet these are the historical folks paladins are modeled on and arguably could be part of the paladin spectruum.
If you have a well considered concept for a paladin and play it true to that concept, I'm not (nor is my group) going to tell you that it's wrong or it isn't really LG. You might provoke some interesting discussions after a few beers and there are limits.
As a side note, my wife who tried the game for a campaign but never got into D&D still finds it a useful notation when we discussion fiction or historical characters or talk about her own writing. As one way to model human behavior, I've always liked it. I've never, even in my distant youth, though alignment languages or alignment as a quasi-religion made any sense but I like it from the sense of: lawful-chaos tells you how much a character considers the rules and conventions of others in their actions, good-evil tells you how much the character considers the well being of others in their actions. And yes, this is an "in-the-characters-head" definition alignment but that's useful for RPG.