Unlike Youtube, Netflix doesn't get paid (by advertisers) by the amount of time you watch it. A person, like me, can be happy with his Netflix service even if he watches it "just" 30 minutes a day, and even if this person spends other time watching youtube, or, god forbid, sleep.
For me to remain a happy Netflix customer, it doesn't need to swallow up more of my time or compete with Youtube. It needs to continue to show me things I *want* to see (it needs to increase the amount of content it has - especially "older" movies and series, not just new made-for-Netflix content), it needs to remain ad-free (respecting my time) and it needs to remain cheap, and needs to remain convenient (watch on my phone, watch offline, etc.).
By the way, Netflix could fairly easily steal Youtube's thunder, by allowing popular content providers (e.g., those already successful on youtube) to upload content which will be shown on Netflix, in return for $0.002 per view (I think this is about what Youtube pays the content uploaders). People will still use Youtube to listen to illegally-uploaded songs, but to watch original content, ad-free, they could go to Netflix.