No it's not. Alpha/VERY EARLY Dev is almost always under NDA but Beta rarely is.
Every closed beta I've been has featured an NDA up to a point, with *I think* the exception of Tribes Ascend which took a different route entirely with the option to simply buy the game while it was still in beta.
A large % of people who get into betas do so for having a blast and some fun and almost never submit any feedback whatsoever.
That's definitely a factor, but that doesn't mean they don't submit
any feedback, or that the feedback provided isn't of sufficient quality and quantity. Simply having a controlled number of users logged in and playing is also useful.
What purpose does keeping a beta of a game under full NDA when you have so many people in it and everything will leak anyway?
Controlling the image/public perception of a product leading up to its release and through its lifespan is extremely valuable!
9 times out of 10, the average gamer/internet user will only be motivated to post publicly about something if he has an axe to grind. Not many people feel the need to announce the fact that something they're using is working perfectly fine and meeting their expectations. And why would they? My laptop's working fine right now, I don't need to tell everyone about it. Yet when I googled it I find a lot of complaints, lol.
As you mentioned, a lot of people will sign up for a beta for purely selfish reasons. Then they find that they're not getting the free ride they expected and post opinionated, uninformed, butthurt rubbish. And then people read that rubbish and believe it. Just a few pages back there's a guy having a good old moan that everyone drives tanks and the game is really boring. Followed by at least 1 comment along the lines of "oh, shame that - thought this game was looking great".
As for the NDA being ineffective, I also disagree with that. It's not just about the individual. A bit of googling for PS2 stuff shows some "leaked footage" removed from youtube (though still existing on a torrent site), an announcement on planetside universe saying they'll delete NDA-breaking posts, ditto the planetside subreddit, and a bunch of planetside forums all saying the same thing. Of course it's impossible to 100% stop info leaking when you get the general public involved but it does mean the majority of leaks don't stay around for long.
Dropping the NDA after the game is mature enough that the positive discussion drowns out the negative. Stopping public forum crying while the game's still in development; or at least allowing the positive to balance it. Having the top google and youtube results all showing your own content and community/media websites and features instead of forum cryfests. How can you say that an NDA has no value and isn't needed?
Public betas, which is what PS2 beta will be, invite or not do not need NDAs. Everyone and their dog just likes to slap an NDA on everything these days, gives them a get out of jail free card to censor anyone and everyone without lashback from the community for it.
For reasons outlined above - I disagree.