I don't think that the number of alignments is the relevant difference.
The relevant difference is that 4e, unlike previous editions, has almost no game effects related to alignment.
There is no Detect Evil spell, for example. In fact, Paladins go from being able to detect evil at will to being among the few people whose alignments can be easily known (assuming some basic religious knowledge, if you know the God's alignment and the Paladin's God, then you know the Paladin's alignment). Clerics (at least single-deity Clerics) of Aligned Gods can be detected as (God's alignment or Unaligned).
There are no weapons/spells that do more damage vs. Evil or Good opponents.
Alignment is now nothing more than a personality marker, like the other personality traits listed on 23-24 of the PHB. If a character is religious, each god has specific goals that the god wants furthered, as opposed to a generic "be good" or "be chaotic evil".
In fact, this makes a change in metagame knowledge. The players might know that the orcs are Chaotic Evil, but the characters just know that the orcs are trying to kill them and the innocent villagers around them. If a character sees a new monster and their knowledge checks fail them, they will have no clue as to the monster's predisposition until the monster acts. Heck, at best knowledge checks give you "typical temperment" which is not the same as alignment.
So for those that want alignment out of the game...it pretty much is. I mean, lift the restriction on Cleric and Paladin alignments, and replace with the "orders from the god" (conveniently listed with each God) and you are done.
