Here is a blog post (2010) describing the decision to move out of our own data centers:
https://medium.com/netflix-techblog/four-reasons-we-choose-a...
So they already have their own system. As as some below have mentioned, they could simply move to Azure if they wanted without much trouble.
That's not to say it might not be a worthwhile approach over the long run but it would be a huge strategic investment in something that has essentially nothing to do with what they view as their core differentiating service to customers.
Would Netflix have done things differently if they had known they'd reach this level of usage? Perhaps. But disentangling now would be very difficult and almost certainly disruptive--including a likely reduction in quality of service.
And disentangling be disruptive? Stand up your new datacenter and shift your apps over with DNS when they're ready to serve production traffic. If you can move traffic between regions, you can move it between on prem and cloud.
"Netflix will most likely exist even if we don't provide them server services as there exist other cloud providers and / or Netflix is big enough to roll their own, so we might as well have a piece of our competitor's success by having their infra spend come to us."