I am less inclined than most to be concerned about kids only watching what's on nexflix these days, despite a great amount of hand-wringing on the subject. The reason is simple: I used to be one of those people. Approximately ten years after I recognized this as a potential issue, I've seen 76 of AFI's top 100, and 53 of Sight & Sound's top 110. There are a few issues being conflated:
1. Access: part of the reason my film education was so poor prior to 2003 is that movie distribution was poor. The movies I had seen were for the usual reasons: a smattering of classics available at the local video store, a few VHS tapes my parents had bought or would rent from the library (the latter of which skewed towards Merchant-Ivory and Jane Austen adaptations for obvious reasons), and the requisite freshman year friend who was taking a film class and invited me along to the screenings that taught me the value of foreign films (The 400 Blows, Red Sorghum) and hate Robert Altman. It was hard to get a hold of very many movies at all, much less high-quality copies, so even if I'd had the money and the inclination, my options would have been sorely limited.
There's precious little appreciation that the introduction and acceptance of DVDs in the early 2000s had the same democratizing effect as the introduction of CDs in the late 80s: everyone converted their catalogues to the new format, which meant cheap, high(ish)-quality editions of almost all movies. My interest in music was sustained because I could go into, say, Best Buy in 1996 and get five cds for $25, because they were bands no one had ever heard of, and the store just wanted to get rid of the inventory. I bought Woody Allen movies and foreign films for the same reasons: I had no idea if it was good, but it was $10. This move is also what makes Netflix possible as a business.
It's worth circling back to this: if someone isn't interested in movies now, it's a question of will. But will can be changed, if it's not a question of berating people for their poor choices, worrying about the future, etc.
2. Canon: If there's a logic behind the AFI list, I've never been able to find it. "These are good movies that were made in America" is not going to ease anyone's transition into watching film. Nor Sight & Sound's "these are foreign films that usually have good cinematography." For their to be a "new Netflix canon" there must be an "old non-Netflix canon" it's replacing, except there isn't one. Film has lists, but no narrative: The Cabinet of Dr. Caligari, Gone With the Wind, Annie Hall and, oh, Up are all quite good films, but good in different ways and different genres for quite disparate reasons. A generation of filmmakers might be working in sync with what came before (the Cahiers du Cinema people drawing from noir and westerns), or in opposition to it (the 70s Auteurs versus the studio system); careers are significantly longer and credit is given for doing the unexpected (Tony Curtis in Sweet Smell of Success; Billy Wilder writing Stalag 17), so the fact that Fritz Lang directed it or Marlon Brando starred in it doesn't tell you much. College students looking for an exhaustive-if-limited selection of films they need to watch (something on the stature of Pitchfork's best of lists) have no real options.
3. Points of ingress: The most fortunate coincidence in my years of movie-watching was having Woody Allen be the first figure I was interested in: he constantly makes reference to other films and is not particularly shy about doing so. From him, I found Bergman and Fellini, and thus New Wave and Neorealism, the 70s movies to which his best works were a contrast, and on from there. It takes a lot of time: I watched many westerns until I figured out I didn't particularly like them, and spent a lot of time figuring out I will never care for Kurosawa (Dursu Uzala, maybe). Along the way, there were surprises: Powell/Pressburger, say, or Buñuel, who I didn't expect to like, but did.
4. Let me again state a general opinion that one of the problems with American culture is the idea that all one's tastes have to be set at age 18, if not sooner. I prefer different things at 31 than I did at 21, and would suggest that the process of aging itself has allowed me to like things I would have previously dismissed. That students arrive at college--or leave!--not having sampled widely from world cinema is not a problem. There's a whole life to make that happen.