Independent movie rental stores were viable for the same reason as chains with multiple locations were viable: you needed geographic proximity to customers to rent them movies. While some independent stores may also have had a degree of genre-focus compared to, say, the national chains, IME it was usually a fairly weak focus that reflected the local interests and demographics (and, actually, the chains would stock different titles in different stores the same way.)
A genre-specialized Netflix would have much of the fixed costs of a full-fledged Netflix, would be competing with Netflix and other full-spectrum streaming sites to acquire content, and would have an uphill battle getting the visibility to attract users.
Scale often has advantages.
This was my thinking, though I didn't know if it was correct or not. I made the post because all the big players, even together, don't have most of the great (foreign) films I've seen. This makes it so that my only option is to hope and wait until they do (though the problem is I've already seen them, so the new problem is that I'd want 'related films' for the ones I've already seen). To say 'this film is like that one, you should watch it', they'd need to know what I think is actually good.
An unquantifiable amount of venture capital for infrastructure and licenses.