I love me some 4e. Have had many a good session over the years. However, one thing almost drove me away from 4e before I even got into it:
The PHB Paladin not only has no alignment restriction (I can live with this.), it also specifically told me, the DM that (unlike the cleric), the Paladin's powers were not dependent on a deity's will--once given, the paladin could do whatever the hell he wanted with no fear of any repercussions, save social ones!
And wouldn't you know it, my problem player wanted to play just that paladin. Thanks a lot, WotC! You gave him a rulebook to shove in my face and say, "See!" instead of giving me (and him) guidelines on how to play a paladin responsibly.
As a player (and, somewhat, in real life), I love playing the classic, honor-and-code-bound, walk-the-high-road-at-all-costs paladin. I really would have liked some indication in the PHB that I still had the right to view paladins as such in my campaign. (The essentials cavalier did correct this mistake, by the way.)
That said, I have long viewed alignment as a nebulous thing (even when tied to game mechanics. For instance, in 3.5e, I turned detect evil into an always-on effect and simply let the paladin (different player, actually playing a lawful good paladin) know when "that guy doesn't seem right."
Therefore, I'd have to say that alignment restrictions are not a must for me, but behavior restrictions for some classes definitely are.