I can't find a definitive answer to whether putting up your game on Steam via a publisher helps somehow, other than bringing some popularity due to publisher's other games/apps. It seems that Greenlight procedure doesn't change or speed up if you have a publisher, or decide to publish yourself (at least according to Steam itself, officially, but who knows what goes on behind the scenes).
The general sentiment on the internet seems to be that you should "cut out the middleman" and save your money that would otherwise go elsewhere, for almost nothing.
People are comparing the Steam publisher to other game, music and video publishers (networks), saying they exist to help distribute your product by making physical copies (optical discs, usb drives, third-party stores), but this doesn't seem to apply to Steam, as there's nothing physical involved.
There's also a matter of advertisement, community management and posting news, updates, etc to create more visibility, which you can also manage on your own, if you wish.
So besides that, are there any important benefits to having a publisher on Steam?