But the only reason their history differs from ours, in matters large or small, is because they follow a different moral compass. The practical aspect of Mirror existence is
that you have to expect the worst of each individual. By our
standards, and by those of our "regular" heroes, they're spoiled goods all.
how convenient it is that out of the infinity the writers pick one where that rare moment is occurring!
Convenient, yes. Unlikely - not really. Because it's the very intersection point that makes the contact happen. There would be no contact between a universe that is lacking a Benjamin Sisko and wants to kidnap one, and a universe that has no Benjamin Sisko to offer; the intersections necessarily only happen when they can.
Apparently, the very concept of Mirror interaction hinges on it being dramatic (not surprisingly!), and for some reason no humdrum interaction can ever happen. But this can easily be phrased in typically vague Trek/scifi terms of specific people from different universes attracting each other. Or holes left by people doing the attracting, much as in semiconductor physics.