Though D&D has been my favorite fantasy game for quite some time, I'm not really bothered by alignment going by the wayside.
As it is, players will act as they will, and problems will stem from that accordingly, based on the situation in-game.
Star Wars has Dark Side points for Dark Side-worthy behavior. IMC, I expect a couple of my players to do something that will earn them a Dark Side point. In one case, it's because the player's emotions cause that person to often act without thinking. In another case, one player will argue about getting the Dark Side point because it wasn't "technically an evil action" (but rather, the player's arguing because that player is getting a penalty for something). Though I sorta doubt it, I wouldn't be surprised if I have to take up someone's character because they've fallen to the Dark Side (FYI: received a number of Dark Side points = to their Wisdom score).
Quite a few players, in my experience, gravitated toward Chaotic alignments, and CN is the alignment of choice for many of those players (esp. when Evil ALs aren't an option). However, IMO, the games often suffer because of this because everyone's busy acting like the tough guy loner or the carefree trickster who doesn't need anyone instead of actually working as a team (which is crucial in D&D, esp. since each class covers a particular role). It gets old, quick. These players have sometimes said that they're tired of playing the noble hero role because it gets old, but instead they go and play another well-worn stereotypical style of character instead.
And, these styles of play will continue, whether D&D has Alignment or not. Even with the "light dusting" of Alignment in game, there will be points where the game breaks down into an argument.
But, rather than making it a built-in framework of the game system as it has been, I think it'll be a bit more discretionary for DMs to work with. Now, I wouldn't mind certain class options, magic items, and the like still using these remnant Alignments as requirements somehow (such as only a Good character can use a holy sword, for example). But, I woldn't be bothered at all if this was the exception rather than the norm.