Its only going to happen if the Devs decide to walk back years of intentionally
balancing PVE and PVP together. And, no, it doesnt matter how many issues you see with their implementation of that up til now - its imperfect like so many things in this game. But it comes down to the Devs and their vision. It entirely possible to transition from PVE to PVP and back, though you need different builds to be optimized, just like you would for transitioning to different levels of PVE content or PVE roles.
From the viewpoint of a once PVE-only player, separation from a PVE perspective is essentially "I want this game to be able to be played as a single-player TES game, with the option to do group content with my friends."
From a PVP perspective, seperation is essentially "I want this PVP game to play like other (better) PVP games on the market.)
Now, I cant speak for the Devs, but...
For one, I don't think the Devs are interested in competing with other PVP games in their own field. Or even interested in competing with the single player TES games in their own field. Nobody ever nerfed me in Skyrim.
Two, separation means giving up a chunk of PVP players playing PVE, and vice versa. PVP players no longer have to grind Undaunted and gear from dungeons/trials? Woot! Oh, and PVE players no longer have to grind AP for caltrops, warhorn, and Vigor - and PVE players better hope ZOS still lets you use Alliance War skills in non PVP areas. Why would ZOS want to give up players playing parts of their game, even if the players dont enjoy it? Ever since One Tamriel really, ZOS has intentionally designed things to forced players to play ALL of the game if they want ALL of the stuff. Feature, not a bug.
Three, ESO is an MMORPG. Its designed like an MMORPG. Its designed for group content, both in PVE and PVP. Its not designed to be a single player TES game with optional grouping. That its become that in PVE is a pretty alarming problem. For one, it means that some PVE players think they get to do everything in the game without having to adapt their builds to the situation. We see this when those players enter dungeons and PVP. Second, it means that a lot of the MMO-type game development seems at odds with the RPG-side development, which results in frustration for players who have much more experience with one or the other. Third, most players, if not pushed, are happy to stay in the niche of content they know they like. ZOS is really good at pushing players out of their comfort zone and getting them to at least try content. Look at the line up of Festivals - Witches Festival is every type of boss this year for the dremora motif, Midyear Mayhem is all forms of PVP, Undaunted Festival is all group dungeons, and the Anniversary festival is all types of dailies. Festivals are just one example of ZOS, deliberately, trying to get players to try out all forms of content if they want ALL the rewards.
Finally, ESO' vision for PVE and PVP has changed in the past, so its not like it can't happen.
First, PVP was the end game. The only endgame. You did your faction questline, you went to Cyrodiil, and you fought,
Then, ZOS introduced Cadwell's Silver and Gold as the end game, because shockingly enough TES fans want to quest, not just fight.
With One Tamriel, ZOS opened up the world. Now, overland quests are basic content. PVE has end game dungeons and trials - which contains gear and skills needed for PVP - which contains AP needed for skills for PVE. PVE and PVP are in seperate zones (though Cyrodiil and Imperial City retain traces of when ZOS thought everyone liked mixed PVP/PVE zones), but the gear, skills, passives, and experience you need to do well in both are acquires in both PVE and PVP. Its designed to keep players playing both sides of the game and all content within the game. If you want to get all the things in ESO, you have to do: public dungeons, group dungeons, quests, Cyrodiil, trials, arenas, battlegrounds, and dailies. Thats by design - a giant rat race to keep us busy playing the game and the money flowing in.
Separation, for good or ill, would result in big changes that the Devs would have to okay.
For PVP: They'd have to fix the lag and performance issues. Without that, PVP is dead.
Beyond that, everything that is obtained from PVE has to go. No more leveling to 10 before PVE. No more mount training, no more gear gathering from dungeons, no more Undaunted grind. Everything for PVP is obtained through PVP activities - maybe ZOS gives a PVP version of those things, maybe they don't.
The devs begin developing a PVP only team which is separate from the PVE side of things. PVP now needs its own new content, since its players may or may not still bother with dungeon packs, etc.
Also, this moves ESO directly into competition with other PVP games on the market, and well, good luck with that.
For PVE: obviously, PVE loses the Alliance War skills. Maybe the devs gives a PVE version of those, maybe they don't.
The Devs start balancing PVE against itself, and since the Devs are in an MMO and still need to keep players chasing the carrot of the meta, the nerfs continue. Or the devs stop nerfing, power creep ensues, players get bored, and leave, because once youve finished all the content in a single player game its got limited replayability. PVE becomes more like a single player TES game with optional grouping for end game content. Basically, ZOS continues developing PVE exactly as they do now - nice new zones with lots of grindy dailies, dungeon packs, and mini-trials.
TLDR: A separate PVE is a single player TES gsme with less mods and optional grouping. A separate PVP has to,compete with other PVP games. Why would the Devs want to do something that encourages players to play less of their entire game?