That might have worked, but it would have distracted from Worf's story. And Sisko and Dax would have required additional speaking parts as glorified extras. A story focused in that type of universe might have worked. I was never that thrilled with the show crossover appearances in "Birthright", the DS9 characters should have been more involved with the plot. Or they should have set up a 2-parter in TNG, with the conclusion told on DS9's show.