But busy is way more restrictive than just simply being not found in player search. (Which is the original suggestion from the OP) A blacklist has a maximum amount of people you can put there so if people that want to play without a FC and have to black list even such players will have a full list quite fast. Its true that with blacklist you might not see anything a stalker writes but that does not change the fact that they can stand near you, follow you maybe even see who you are with and so on. And they can stand near you and shout out bad things about you, while you have no chance to see this. Not being on the search function will at least stop it partly since they wont be able to see where you are anymore thus making it way harder or even near impossible to stalk you. At the same time if you are busy and your FC wants to do some group content you are unable to join them. Not every group content is in an instance so if you want to join them you will have to take the busy status away again.
And lets not forget all the new RMT invites. Those would be gone too. Even just for this, a new status would be nice.
IMO it's just another icon next to your name, so nothing game changing and yet it can at least make the game more peaceful for some or even a lot of players. You would only need to activate it with on click and you are mostly free from spam while with blacklist you will have to go active again and again and thanks to the new RMT method you also have to go around and decline the invites too..it may not be much work but why not have some new little features that will make it much more peaceful and comfortable for such people thus giving them more joy in the game? I mean this is in a way only bad for those that send out those spam invites or are trying to find someone for some reasons..So in a way it has no true downside imo. So even if it improves the situation only a little bit or just make something more easier why not have it ingame?