But we already had an alternate-universe version of the events of the first movie in "Mirrored." I don't think it's likely they'd just repeat themselves like that.
That is exactly the reason why I believe they fill repeat it - to follow the pattern. The stories in general are retellings of TOS episodes, and "Mirrored" was uncomfortably close to In a Mirror, Darkly
If the alternate reality crew meets the genderverse crew through another 'lightning storm'-like black hole, it would be the third such event in the A.R. timeline. Whenever somebody would mention it, they'd might say something along the lines of: "Remember the lightning storm? The Kelvin
event. Spock's return. Our meeting with Jane Kirk."
Because there's no guarantee the movie would acknowledge the comics, the comic writers have to write in such a way as to avoid their events coming up dialogue and be discredited, which we already saw happen with the line "Nobody died under my command."
Another reason is that the black hole-theme is linked to the Narada
and accidental time travel. In the genderverse the equivalent of Nero's rampage hasn't occurred yet. It may happen now.
Apart from those reasons, I'd love to see a cross-over. Maybe they're doing it exactly because there was none in "Mirrored".