Counter points:
1) 2007 was a superb year for "great" movies, with Zodiac not even getting a Best Picture nomination, and I consider three movies that year to be bonafide modern classics: Zodiac, No Country for Old Men, and There Will Be Blood. I could write a think or three on the brilliance of No Country/Coen's/Cormac's vision of the "death of the West", as captured so achingly beautifully by Tommy Lee's closing monologue. Best Picture is subjective, just like everything else when it comes to taste. Remember, Paul Haggis has a Best Picture statue for fucking Crash.
2) Children of Men is about as good of a modern sci-fi movie you can ask for, with some of the best technical cinematography this century. It's a terrific film, strong on narrative, cinematography, acting, errthing. It's great.
3) In the last five years, I'd feel comfortable calling these films "great": Arrival, La La Land, Moonlight, Inside Out, Spotlight, Boyhood
4) Since 2000, great movies: Eternal Sunshine of the Spotless Mind, Mulholland Dr., City of God, The Lives of Others, Sideways, Lost In Translation, Spirited Away, Memento,
5) There are some sneaky-good films out there I'd hesitate to define as great but are damn good and signal a future for great filmmaking: Whiplash, Her, The Nice Guys, The Florida Project, Hell or High Water, Wind River
tl;dr: movies are still pretty damn good