I personally think this is a phenomenon that will diminish in a distant future. The reason is that the gaming industry as a whole seems to stretch out on how far they think they can push this thing. Indies go for early access, but even some AAA-studios seem to release stuff in unfinished state. The end result is that any hype surrounding 'release day' get milked to death.
I don't get the appeal of playing around in a buggy state that may or may not crash my pc, and is missing serious parts of the content. In my UT2004 days, I beta tested quite some maps and gave feedback to the mappers. I liked doing that and had some influence on the end product. But it came at a price. Or rather: two prices. One was that a mapper did not always agree or being able to change it to your liking. On games, I figure this'll be even worse. If your game crashes, you're mentally obliged to fill in a bug report, but that's not always clear (just writing 'it crashes' isn't helping them much). So you spend a lot of effort doing something that is basically work. Not that there's anything wrong with that, but then there is that second price to pay:
playing early diminishes any chance of wonder and excitement. By the time those maps were published, I was already tired of them. And where others saw something awesome, I mostly saw the grey-ish walls that used to be there.
I've only bought one early access game thus far (contraption maker), and that was after reading enough about it to have confidence that it was pretty stable and was nearing public release. I'm glad that gamble turned out correctly, but it's a lucky gamble.
What isn't mentioned so much here is that there's a plus side to early access. Bug fixing is one (though I have my doubts on the effectiveness of it). But in games where the user is expected to create some content from himself, that model could be awesome. On contraption maker, there are already many dozens of fun contraptions and puzzles. That new unreal tournament will probably have ten times the amount of custom levels than stock ones (as it stands, they barely have anything but a working engine and editor). And I haven't followed minecraft, but it wouldn't surprise me if most of what's being built there is just being built because they were inspired by the efforts OTHERS had already put into it. In other words: if everyone had to wait until release day, everyone would've seen a pretty barren ground and just leave.
Oh, and...
relevant edutainment video...click me, click me! 