There used to be such a system, but it had to be discontinued due to abuse by people who just wanted games for free, apparently. Edit: but it was never removed from the site, that's why people can still stumble upon it.
Are you sure? Not only can you still apply - people are being accepted.
Application:
https://itch.io/partners/application
Partner List:
https://itch.io/partners/list
The last accepted user was 5 days ago.
It states that these users can access "a large collection of paid games" I was prepared to enter my game into this system assuming it was people who at least had some kind of platform but it doesn't appear to be the case.