Maybe you're confusing Netflix with Amazon, who do offer Starz as an additional subscription? Or maybe you're just conflating the Starz catalog with Netflix's streaming service, which was originally part of the DVD service and then became its own thing?

We used to have a really long list, and still we'd find stuff that wasn't on the list that we decided to watch instead because it all sounded good. Over time, we only got to watch a a fraction of the stuff we'd added to the list, with the rest simply disappearing.

This isn't just a "feeling," it's both an actual phenomenon and to some degree a deliberate choice on the part of Netflix, which wants to focus on its own stable of Netflix Original content that it won't have to renegotiate for every few years. See, for example: http://screencrush.com/yes-netflixs-film-catalog-has-gotten-... (and note that the "before" number in that article is from after Netflix lost the whole Starz catalog!)