People pay extra for premium channels to see GAME OF THRONES. People sign up with Netflix to see DAREDEVIL.
Doesn't seem to hurt the shows' popularity any.
HBO and Netflix have a reputation for high quality original series. CBS All Access has a reputation of laggy back episodes of Survivor. And both of them were focused on movies before they ever had boutique original programming.
If the new Star Trek is as good as Game of Thrones, people will pay to see it. Even Star Trek fans are going to go in really skeptical. If their friends come to them raving "THIS IS THE GREATEST SHOW EVER EVEN BETTER THAN THE ORIGINALS", they will pay. If they say "Eh, maybe on the level of Voyager or Enterprise", they won't bother and they'll hang tight for an opportunity to watch without paying.
If you're charging upfront for episodes you're betting on quality, critical rep and word of mouth. Do you honestly expect a new Star Trek series to have those things, or do you hope they *might* have them?
On the other hand, before South Park, Comedy Central was pretty much an SNL repeat delivery system. So you never know. I don't even know what the hell Fox was showing before The Simpsons.