Why would anyone use SteamOS when they can just use Ubuntu (or whatever distro) and install Steam?
You are asking the wrong question. SteamOS does not try to offer more than a linux distro can offer. It is only a way for valve to enter the living room gamig market, essentially becoming microsoft's competitor without being tied to windows at the same time.
Anyone who already uses a linux distro with steam client installing on top can happly keep on using, valve losses nothing, but thet needed to provide their partners with an user friendly OS they could ship installed on the machines that was not tied to microsoft, it is as simple as that.
In a nutshell, steamos is not targeted at anyone capable of choosing and installing an OS themselves, its main target are those who will be buying a machine with the OS installed, plugin into their TVs and start playing.
Eventually valve will probably introduce improvements to the OS, that most distros will simply incorporate if they want to keep compatible with steam.
But, from what I know, SteamOS is just another Linux distribution. It doesn't even boot up to Steam, you have to manually run it.
Last I checked, Steam (big picture) started automatically. If you did the Custom install without following the second set of instructions though (last I checked), you'd boot into desktop mode.
As for why to use it... it would probably be best suited for a HTPC sitting and serving a gaming-oriented purpose mostly that you don't have to worry about breaking out of nowhere due to some non-gaming-related update. You'd turn it on, it'd boot Steam Big Picture, you choose a game, play, and then shut it off when you're done; basically like a console.
To be fair though, you could just throw something like Ubuntu on a HTPC, have Steam auto-start, and have it start in Big Picture mode for a similar experience; although the chance of it breaking due to an update (although rare) is probably higher.
I guess it just depends on the usage scenario and how much care you're willing to put into maintaining the machine. If you just want to game without much intervention at all, SteamOS seems great.
To be fair though, you could just throw something like Ubuntu on a HTPC, have Steam auto-start, and have it start in Big Picture mode for a similar experience
Nope since on regular Ubuntu you can't just click the "Update SteamOS" button in BPM and have it update everything from Valves repos in the background. Nobody would want to exit to the desktop just to update the OS everytime on something that's designed for the livingroom. Yes the cool people would just ssh into it from their Android phone jada jada...