Organized play (and Class Decks) are not mandatory to introduce Multiplayer but they are simplest and easiest solution, one that have least chance of introducing bugs that could make Story Mode unstable. Could it be done without it? Sure, but that also bring the risk of creating "another Quest Mode" with all it's problems and issues.
I'm not against the introduction of class decks to add more content to the game, but I'm not sure what problems they would solve regarding a multiplayer mode. As the poster above noted, the way that decks are built from the vault there are a "nearly limitless" quantity of campaign cards, and a "technically unlimited" quantity of Blessings of the Gods. Class decks tried to help support organized play and pick-up games by segregating cards you own from the hosting base set. There is no analogous concern in the digital app, the vault simply rebuilds itself before the next game.
Treasure cards are a concern, but they could either be turned off in multiplayer, or a system could be created to allow you to "keep" treasure cards you don't own. The latter option seems like it could be abused, but looking forward with the PC version of the app, it honestly seems that the devs are less concerned about Treasure Chests being core to the revenue stream.
What is problematic for async multiplayer (synchronous too), is that there are still a few communication and gameplay issues to smooth over. Multiplayer might be simpler if each player just did their thing independently of the other, but Pathfinder doesn't fit the "Words With Friends" gameplay model. Figuring out how Player A can beat a check requesting a blessing assist from Player B and maybe having Player C volunteer to play a spell they were holding onto for emergencies it going to be rough. Having a turn stalled-out because the person controlling Player B is in the shower (and you really need that blessing) won't be a lot of fun either. If I recall correctly, the recent Pathfinder dev stream briefly glossed over that issue, stating that should multiplayer be implemented someday, maybe some rules would need to be modified or simplified to fit an async model.
The Quest Mode/Story Mode crossover bugs weren't all that terrible in reality. However, they were catastrophic in that users couldn't do anything to resolve them and helpful cloud syncing only made things worse.
As one of the devs mentioned over here, when their small team had to chose between troubleshooting/developing quest mode or ensuring the core experience (story mode) was as seamless as possible, they chose to cut quest loose.