The reason they can rent-out DVD titles from anyone, is because of the First-Sale doctrine[1] in the US. Basically, once they buy the DVD, they can do with it what they want. It's the same law that lets libraries operate.
With streaming, they need permission of the copyright holders. Who, at first, were all "Who gives a shit about streaming, it doesn't make any money and the quality is shit". Once Netflix proved out how to do it right - then all the studios realised there was money to be made by doing their own platform (even if you do a shitty job of it)
Conversely, since NetFlix's DVD service doesn't have any competitors they could get away with having a crappy selection, but they have a great selection, and it's been great for at least a decade.
So it still doesn't make sense.
The movie selection on NetFlix's DVD service[1] is still fantastic.
The movie selection on their streaming service[2] is absolutely atrocious.
Not sure what accounts for the discrepancy.
[1] - https://dvd.netflix.com/
[2] - https://www.netflix.com/