Since the dawn of Netflix's original programming, their library has shrunk. Back in September, Exstreamist reported that since 2012, Netflix's streaming library has shrunk by 50 percent. That's a reduction from about 11,000 titles to roughly 5,200. However, that doesn't mean there aren't good movies available and it doesn't mean you can't try to influence what they acquire.
At Netflix, there's a somewhat difficult to find page titled "request TV shows or movies." At that page, you can enter the title of movies and shows you want to see. Though, they don't guarantee your request will produce results.
Immediately after you submit your suggestion, the site populates a list of reasons they may not be able to add the title. They specifically list Game of Thrones as an example of something they can't add to the library because they've clearly had way too many subscribers ask for that one. The reasons you aren't getting your wish include that a show may be exclusive to another company (a la Game of Thrones), the "streaming rights are not available," and "other factors" like "popularity, cost, or seasonal or localized availability."
They've also clearly had some repeat customers because they specifically note that you don't have to re-submit your ideas. If you've let them know you can't live without Big Man Japan, they passive-aggressively suggest you "sit back and relax." "We've received your feedback and there's nothing more for you to do."