Steam has Greenlight now, so you don't have to be "vetted" by Valve anymore.
There are many other services already though that provide similar functionality, such as indie game stand, desura, etc. that have none of the restrictions you've mentioned as being a reason to not use Steam.
Greenlight is still a vetting process, just with a different mechanism. Suggesting that anyone can just get their game on Steam is flat out wrong. Really well made and polished games (see: Midnight Mansion from ActionSoft) fail to get noticed through either process all the time.
I have nothing to do with this service but I find it definitely compelling. Indie Game Stand only features one new game every four days (so even if you're accepted you likely have to wait to launch.) As for Desura, that looks like another good option, but is still quite a bit more involved.
If I made a game (a 48 Lundum Dare game like in the example page, for instance) and just wanted a way to put it out there immediately with little effort and no need to join a community or anything, itchio provides that option. That's what is compelling.
Those are things that might be compelling to the content creators, but I'm not seeing much that's compelling to consumers. (And I'm not convinced that there isn't already another similar service that also addresses those concerns.)
As the others pointed out, most of us don't want yet another game distribution service -- we already have a few.
From a consumer point of view it isn't a game distribution service (at least I don't think so.) I make a game and I tell some friends about it or post about it on my blog and link to a page where they can find out more info and "buy" it (or grab it free if they prefer.) From the consumer point of view it might as well be a page on my own website, they don't care. When I bought FTL I went to the FTL web page and paid them $10 and got the game. I didn't need to join any communities or discover the game through a community or anything. This seems similar to that. (FTL offers redemption of the game on Steam as well, but that doesn't matter to me.)
[ As an aside, FTL is apparently on sale for $5 for the next couple days. I recommend this game to anyone and everyone who ever enjoyed an episode of Star Trek or Firefly.
Agreed, to me it seems that something like this has the potential to become the "Bandcamp for games."
Steam, even with Greenlight, is intended to host a curated selection of games. That is part of (or at least it traditionally was) Steam's value to consumers, but it has the side-effect of introducing bias against small, rapidly-developed, prototypical or otherwise less-polished games.
Here's a niche: Some people make neat game prototypes for competitions like Ludum Dare with a surprising amount of potential. Not everyone can afford to quit their job to turn their prototype into a well-polished product that can succeed on a popular app store or be crowdfunded (nor is every idea mainstream or even good enough to warrant that), but they are probably capable of at least cleaning up their prototype a bit and adding a decent set of levels or other content.
If someone makes a generic but fun game for Ludum Dare (say, a pixelated-platformer with a gimmick), I'd probably be willing to toss them a few bucks, mostly out of good will, for a more-polished but still quickly and cheaply developed successor. Whether they use that money towards developing an iteration that can succeed on a popular crowdfunding site (which are being quickly taken over by marketing experts) or as pocket change is fine with me.
This use case could be even more well supported by a Bandcamp-like donation system (which is what "pay what you like, or nothing at all if you are aware that you are allowed to enter $0" effectively is).
I'll end my reply by wondering aloud if a new generation of freeware games would ever be viable -- high-quality niche games released for free (and possibly open-sourced), and supported by a no-strings-attached donation scheme.
I attended a talk given by Gabe Newell at my university back in January, and in it he mentioned that he wasn't satisfied with it and they might phase it out. So Greenlight may not always be there.
Did you listen to his other talk where he mentioned that he felt like anyone should be able just publish a game on Steam using their APIs without approval?
There are many other services already though that provide similar functionality, such as indie game stand, desura, etc. that have none of the restrictions you've mentioned as being a reason to not use Steam.
So again, what makes this service compelling?