It's tough. For the streamers themselves, they cultivate community and a following. Even if they "don't want to" they still have to to some degree as part of their job. There's little doubt it does at least shade their experience of the game, though, as they get access to all of the help they want/need, instant cues for everything regardless of what role(s) they play, guided walkthroughs of pretty much all content, even if it's some of the hardest in the game, etc. (And no, big name streamers doing Ex or Savage content with a team of 6 people who have already done the content doesn't really count as them "blind progging" it as some have suggested elsewhere). I can imagine that some of the streamers would rather experience the game as a nameless face but to do so would basically require they don't stream their experience at all. There's really nothing SE can do to hide their identities as even if they never show their character name on screen or stream with a delay or something it's easy enough to figure out where anyone is by location and appearance alone.

For the "fans" though? Yeah, I will absolutely agree it's pretty "cringe" and pretty embarrassing. It's one thing to welcome a streamer to a new area of the game like if they are entering Ishgard for the first time. It's another to literally follow them around and be there standing at every single quest giver and dungeon entrance. Or to "follow along" and create a new character to "replay the story" exactly as the streamer is.

Of course, those who follow any streamer around and actively try to harass them or negatively impact their experience should be banned, period. That is completely separate from the obnoxious fans or embarrassing hanger-ons. Not only are you breaking ToS but, even if you weren't, you're just making the game and the community look bad. I don't care if you don't like the streamer in question but trying to harass them or drive them away somehow just makes you a.. jerk.