Agree to all. I've wondered about this for a while. It seems Netflix works well if you're real particular about what you want to watch, but if you just want to "turn it on" and hang out it sort of struggles. I have to make a conscious choice about what to watch. I'd love to see an update wherein their search engine starts playing something in the background based on what I've watched before or what they think I want to watch. To be honest, I'd love to see Netflix be way more aggressive in marketing too. Sponsor the World Cup or something...truly free me from cable by giving me live sports. The NHL is struggling in a lot of markets...start carrying them (Bias admitted: from Minnesota). I've "cut the cord" for 3 years now and I still have to sneak a way to watch baseball/football/hockey through other people's cable boxes. I think sports might be the way to truly break cable for Netflix.
I've been working on a side project for just that problem! Basically it sticks a programming guide on top of Netflix (and soon Hulu/HBO Go/Youtube/etc) and just autoplays a random shuffle for the channel you choose. It's still really early stage, but you can check it out here:
Maybe there is a market for what you are suggesting, but I like On Demand services like Netflix because I get to pick what I want when I want. Netflix is decent at suggesting things to watch based on my viewing history, but I have never been in a scenario where I wish it would just start playing something for me. I don't want Netflix to play stuff for me, I just want them to keep adding/making new content.