Why do these tabs exist on Lodestone?

[Enkidoh]

Wrong
The purpose of a path companion was to have a NPC partner who fight with you in instanced mainstory solo quests and speak for you in mainstory CS. They didn't exist outside of the mainstory.

The best about them was that every companion race and gender had their own personality.

The male Lalafell who fears his own shadow, the female Lalafell who speak in rhyme, the (female) Miqo'te who is full with love.

Exactly, and the purpose for that was due to the fact that in 1.0 you could start the game as any class in any city - even as a Disciple of the Hand or Land (and theoretically have gone through the entire game as a crafter or gatherer). Naturally this would cause problems trying to advance through the story, so the game had alternative means of getting past difficult boss encounters, the Path Companions who would fight for you was just one such means (others were story npcs showing and doing the fighting for you that you directed and the Parley mini-game being a means to convince the enemy to actually flat-out give up without fighting.)

ARR changed things in that there were greater restrictions on what class you could choose at the start (in other words, a Disciple of War or Magic only), which rendered these alternative methods of story advancing obsolete. But I'd still love to see the Path Companions return as an alternative to chocobo companions, they just had so much more personality.

[Bluevann]

Why are path companions gone SE!

It's buried somewhere in the live letters, but Yoshida explained that Path Companions were removed to give spotlight to NPCs in instanced battles (think of Thancred against the voidsent in the lv5 instanced battle of Ul'dah, Y'shola in the Lominsa one, and Papalymo & Yda in the Gridanian one, but also all the others in the class quests etc.), as well as the chocobo companion. He said to implement the path companion back would be redundant at this point, as there is really no need of them.

[Wobble]

If they can't make them work for whatever reason, they should just remove them honestly.