Until streaming moves towards a model of allowing you to buy the individual movies/series you want to watch instead of having to subscribe to ten different services just to get the few decent things they each make, I won't be doing it. (I do have Amazon Prime, but the free next day delivery factors into that beyond the streaming.)
And yeah, what other people have said about losing all access to a film/show if the provider decides they aren't going to provide it anymore is definitely a problem. No one can take my CDs and DVDs off my shelves. On top of which I own a bunch of music and movies you simply can't stream.