Advantages of owning a Bluray over streaming services:
1) Video and sound quality is significantly higher. Bitrate is higher. Lossless audio. Higher resolution. For people who care about the quality of the movies they watch, this is probably the most significant difference, and until Broadband speeds and penetration is significantly higher, this will remain an advantage for quite some time.
2) Special features. Most Blurays come with special features like audio commentaries that are not normally available over streaming services. You may only watch the special features once, but it does add value to the product and makes the extra cost more bearable.
3) Repeated viewings. There are a good number of movies that I watch at least twice. And even if I don't personally, someone else in my family may or I might even loan it to a friend or family member to watch. TV shows, I rarely watch more than once so I can definitely see this as more an advantage for streaming. But not so much for movies, IMO.
4) Collecting. Some people really like to collect physical media. There is something satisfying about seeing a collection of movies in your display cabinet. And sometimes, you discover that you have some rare gems in your collection that aren't available anymore.
Though I am certainly taking more advantage of streaming media these days, I would hate to see physical media disappear. More than anything, it helps the content producers save money that they don't pass on to the customer. It also helps them keep control so that you can't share your media with anyone else. Instead of giving your physical disc to someone else, they would have to rent or buy it themselves. This is exactly what they want. They don't want you to OWN anything, they only want you to own a temporary LICENSE.