I tend to look at this a little differently, as I think it helps new players especially figure out an interesting character that isn't just a rapscallion.
Rather than Good and Evil, I always recommend that my players pick between Selfless and Selfish. Rather than Law and Chaos, I ask them to choose between Security and Liberty. It might not be the best replacement system in the world, but I think it helps put things into a better perspective for them so I don't have a bunch of "Chaotic Neutral" characters running around fucking shit up, or characters who are just straight up evil and do devious things for the hell of it. It keeps everyone still in that "hero" spectrum because, at least in my campaigns that I run, they aren't supposed to be the bad guys. There can be a lot of gray area, sure, but I don't want to play with characters who are truly evil because it doesn't make sense for the context of the setting, and it can cause some unnecessary butting of heads at the table. I want everyone on the same page, at least generally speaking.
I have played mostly Chaotic Neutral or, in my terms, "Liberal Neutral" characters (I know the word Liberal has a bad connotation now but you know what I mean), because it reflects me more. I haven't had the chance to play too much unfortunately, but that's the character I'm able to play the most realistically and what I have the most experience with. In particular, being a musician myself, I've got a lot of bards that I've used as a player and a DM that follow this alignment.
I DM much more often, so I guess I can speak to one of my NPCs that I really enjoy. He is the son of a god, and is full of hate, willing to do anything with his power to get what he wants. I play him as a "Liberal Selfish" character, or "Chaotic Evil" by normal terms. He hates his god status and wishes to break away from it. I have a good time playing his character, he's full of mystery and intrigue that the players tend to find interesting, but he's still a teenager so he has these explosive moments that show he isn't quite hinged, and doesn't follow society's typical morals.
That being said, this character is still actually aligned with the party on their major goal, which is to take down the god that rules over the land with an iron fist. It's up to the party to kind of help shape him into a hero archetype, rather than an anti-hero one, but he's not some wild character that blows things up and robs stores just for the hell of it. He's got some goals in mind and he'll just use whatever means he can to accomplish them. Alternatively, the party can also forge him more into an actual antagonist with their actions, which my first party to run this campaign nearly did before one of them saved it. It was roleplayed beautifully, honestly.
