Adventurers working together does not preclude the factions skirmishing.
The PvE story in BFA was a direct result of bringing the faction war back to the main focus. I am willing to put actual currency on the table that you'll be hard-pressed to make the argument more people thought BFA's faction war story was good rather than just another recycle of the same plot thread we already went over in Mists of Pandaria, just with a different coat of paint on it, and unlike the BBEG plot recycles, BFA's faction war story left both factions demoralized and disillusioned.Speak for yourself with the 'no good'. I have always enjoyed the conflict between the 2 factions.
And the PvE story does not suffer at all. Alliance players not being able to group with Horde players does not impact the story at all.
The PvE story suffers when everyone involved has to be written as stupidly as possible to make the war plot function, which has been the case every time they "bring the war back to Warcraft." Northrend? The Alliance and Horde provide the Scourge with last-minute reinforcements and progress is made in spite of the factions' involvement, only because the Argents are babysitting. Cataclysm? The Alliance and Horde do Deathwing's work for him, with Garrosh nearly getting the Horde detachment to the Twilight Highlands killed by sending off his air guard to get wiped out by the Alliance on the Twilight Hammer's doorstep and known peace advocate Jaina Proudmoore paints a target on Theramore's back by mobilizing Northwatch and creating a route to easily move siege weapons and troops into the Barrens. Mists of Pandaria? An entire continent is destabilized and sacred ground is desecrated, with a promising launch storyline totally ignored until the very last patch in favor of another generic cycle of revenge storyline culminating in a player faction being subjected to a civil war it never fully recovered from. Legion? The Order Halls have to do all the heavy lifting in the first place because the Alliance and Horde go full retard fighting each other mid-apocalypse, as is their way when the writers run out of ideas.
And then there's Battle for Azeroth, where everyone is either a hand-wringing bystander or a blood-hungry psychopath for half the expansion's life cycle, until Thrall and Anduin remind everyone there's an apocalypse going on and the factions get their annual Flowers for Algernon moment. The faction war is 100% a millstone on the PvE storyline, especially when the whole point behind Warcraft 3 was about the Alliance and Horde getting the hell over themselves after realizing that everything else in the universe wants them dead and Superman isn't going to keep saving the day.