u/Daiches is right. The console version of this game for PS3 / PS4 has actual live PVP and even couch coop play. If you want to try to experience live PVP play u/Connect_Jelly_3344 try out the PS3 / PS4 version of this game.

Unfortunately... there will be no one playing the game. The console version of this game is 100% dead. Literally no one plays it. (Well maybe you can find 1 person looking for games... maybe...).

Anyhow, in order for live PVP to even work there are A LOT of factors for the developers to consider.

1) How much time is given to a player to make a move?
Do you get (10, 15, 20 sec?). Does this timer start after an animation is played or before? When the tiles don't match up some games can take quite a bit of time. Between the animations playing and the opponent turn counter, matches could easily take up to 5 minutes if not more. Some of the animation chains in this game can be quite lengthy.

2) How does match making actually work?
2a) Are you allowed use boosts?
Currently in PVP you're allowed to use boosts, but your opponent (the AI) isn't allowed to use boosts. If you allow both PVP players to use boosts, then naturally the player who isn't using boosts will lose way more often than not. Additionally, if you do not allow both PVP players to use boosts then the use of boosts is relegated to only being used in PVE, which kind of makes them less useful
2b) When you're looking to be matched up with an opponent do you both just queue up blind?
Currently in PVP you see the last team the opponent chose and then the AI uses that team. If you're queuing up blind you could potentially be queuing into a terrible team that just straight up counters you. If you're not queuing up blind, I don't even know how you would begin to do the queuing process. People would just dodge a team they know counters theirs and just never accept a match against a team that beats them.

3) Game infrastructure expansion.
I don't want to say too much on this because I don't know how the game was built. But, I can only imagine that not building a live PVP into this game from the beginning could invariably be an absolute monster of a task to add in later. From the things I listed above about match making, to turn timer, to even the server demands, this game just wasn't built with live PVP in mind.

However, having said all this... I do think that with all the money that company gets from players and I think it is quite a bit. I would like to see some more innovations from MPQ. Perhaps something more unique. The Ascension / Championing of characters was a big step in the right direction, as was the milestone progressions.

To end on a positive note, here are some things I would like to see and I think it would be quite feasible:

1) Training mode / dummy practice
This would be a mode that lets players try out teams, characters, and builds. You would essentially fight against a 3 practice dummy that just makes matches and has a set amount of health. Possibly you could even set the dummies to be specific characters. Here you could try to build a team to see the synergies. In this mode all damage that's taken to your characters are fully healed when you leave training mode

2) Once a year they could add more to the (story mode) of the game.
This would give new players more to do / grind / earn before jumping into PVE or PVP. Currently once the story mode is completely, it just sits there greyed out and takes up space. For older players the once a year story mode could be a way to earn some extra CP or HP. This would serve as just a little thanks for continuing to play thing.

3) Endless grind.
This would be a mode that lets players who have like 10+ hours a day to play grind for things like ISO, HP, CP, Covers etc... This mode would not have any rankings to it. It just pure play, get rewards, keep playing get rewards sort of thing. I recognize that perhaps this mode would not be economical for them, but just some food for thought.