It'd keep users from seeing content on certain streams.

For example, If a user looks at a certain stream to spy on it, you could blacklist them so they can't even view the content the stream has to offer.

*Logs out*

Locking down streams(privating them) technically does that already in a way since people except those that have the link can actually see the stream. That's a good idea none the less.

It would also be helpfull if imgflip added that only the Owners of a stream could send private stream link to other people, and if a mod or someone else tried to give it to someone else, it would come up as invalid, keeping the private stream perfectly safe.
There would be a lot of issues and bugs regarding this though