From the last edition of 40K there was an alliance chart which dictated which armies could ally with each other, some of the factions like Orks and Dark Eldar would only side if the end was nigh. Specifically the term which described their alliance from the book was "Come the Apocalypse". I would describe a Tyranid invasion an Apocalypse. I could realistically see at a stretch the 4 factions in game temporarily fighting together. Weirder shit has happened in the lore, and I'm not talking just about now-redacted codexes. Edit: I know it's fairly tough to justify (Don't wanna ruin that deep Arkhona EC lore right?) but getting into PvE is borderline impossible in the game's current state. Allowing all factions to team up would fix this.
On the one hand, it sounds cool On the other, chaos psychic powers helping space marines and orkoid fluids rejuvenating eldar physiology If the problem is just numbers to form a team, regardless of composition: just make a button that makes you queue for all 4 factions at the same time and drop you into the first of them that gets enough queueing for a group, no?
Considering how it was in the Last Stand with everybody getting rez by the necron overlord, I think we can state it will not be the first time.