It's padding, it means nothing and everything. Every single post where the hair is not down could be tagged with this. Either we imply all kind of tags like ponytail or low-tied long hair to it or we nuke it.
I don't think this tag should be nuked. Without this tag there's no way to search in general for characters with their hair down, since hair_down is exclusively for characters who normally have tied hair. Unless we want to make that impossible, then we either keep tied_hair or expand hair_down's usage.
If we do keep it though, then we unfortunately can't just imply every hairstyle to it. Inklings, for instance, have non-tied twintails; I'm sure there's other weird exceptions but I can't think of any others off the top of my head right now.
I've used tied_hair as a catchall for hairstyles that don't fit neatly into other tags (how else are we supposed to tag post #4908624?) but I agree that in nearly all circumstances it's completely redundant. It probably won't be missed much.
Agreed that this is a bad tag, virtually every hairstyle that isn't plain straight hair will involve the hair being tied in some way. It would be a good idea to try to clean up this search first though:
The ideal use for this tag is as iridescent slime said, and this is how I've used the tag myself before. But there's no way of it ever getting the tag as a whole there and most of the tag is not that.
(edit because -topknot gets rid of far more than -quad_tails)
edit 2: I removed the link to tied hair in the wiki for misty (pokemon) and got rid of the tag from pictures that only had it because of that reason - about 1% of the total content of the tag. Also fixed a few other things in the above tag search.
edit 3: It seems pokemon character wiki creators are very fond of linking the word "in" in the phrase "tied in a ponytail" (or similar) to the tied hair tag.
edit 4: Removed the link from everyone other than Janine. There are still (even after removing a load) 2187 posts in pokemon tied_hair -janine_(pokemon) - you could probably easily remove or replace the lot of them. Which is about 7.5% of the tag.