This might seem attractive on paper, but it's an excellent recipe for burnout and general disenchantment, much moreso than the current RNG-y systems (as much as some of them may suck). You're putting a massive premium on forcing people to log in every single day of their lives for what, three months, and not actually play the game, not do actual questing, dungeons, raids, PvP or any of that jazz, but just GRIND THEIR FACE OFF on a round of Daily quests. People, being rather Pavlovian, will absolutely do that in many cases. But they will not, generally, enjoy it. Many classes/specs will likely have to grind half-a-dozen or more reps every single day, because they have Legendaries which are situationally useful. God help those poor souls - given the amounts of time it took to do dailies in previous expansions they could be looking at 4+ hours of dailies required every single day. Even those grinding just a couple of factions are looking at probably about an hour (unless all the quests for all the factions are in some bizarrely tiny area) or more of grinding every single day. Given many people, even raiders, only have 1-3 hours to play most days (usually making an exception for raid nights, where they might have more like 4 or even 5), that's a huge imposition.
Then, twelve weeks in (or whenever), BOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOM, suddenly everybody and his mother has their Legendary, and if you started the expansion late, or had to change classes or something similar? Welp. Guess you're fucked until you catch up, and you're probably still fucked then, because you'll be so far behind the curve because you just had to spend 12 weeks grinding your face off on Dailies. Even M+ will probably auto-reject anyone without a Legendary in this situation.
And then what? Nothing. Because the Dailies are over. Done. Forgotten. You'll never talk to those guys again unless they sell a consumable or something.
I'm not trying to be mean, but that is a really bad model for how it could work out. I think it may even be worse, in terms of what it does to the game, in terms of the burnout it causes.
I mean, let's try to not even think about what happens the Legendary you face-ground for gets nerfed, and the one you ignored because it was a POS gets buff, and you have a happy 12-week+ facegrind to look forwards to. The total randomness of the current system is bad, but for most players, it encourages them to play a wide variety of content, and to actually PLAY THE DAMN GAME, even if they're slightly surly about it. An MOP-style facegrind would encourage people to do anything BUT actually play the damn game, it would encourage then to just spend weeks hyper-optimizing tedious Daily quests (god help us if some are competitive in design too), and largely ignoring all the rest of the content. Then that grind ends, and suddenly they don't know what to do with themselves. The life they built is gone... and I've seen this with players plenty of times - the grind they were doing ends, and that's it, they realize how burned out they were, and they quit. Maybe they come back in a few weeks or months or a year, but they burn out and quit from this kind of thing.
Oh and another thing - the sheer untold nerd rage if say, one faction with a Legendary "required" for a couple of class/specs had quests significantly more painful to do than another faction? It would be atomic. Faces would be burned off merely reading the rants about it. And it would be the case too, you can guarantee it. Some faction would have Dailies you could faceroll in 15 minutes and be on your merry way, and another would be 45+ minutes of cursing and scouring the area for mobs or clickables or whatever.
Again, nothing personal, I agree with some of what you're saying but Daily grinds of that kind should never happen again. They are a terrible idea.