At least the boring things you do to unlock the boss encounter should be different across districts, I'm hoping.
I'm still definitely interested in the game, just because the premise of the story, the main character's background and the setting all seem fantastic to me, but yeah, I can't help but feel seriously disappointed at the more "open world" game design approach that 3 is taking.
I feel like I'll enjoy remembering and talking about 3 more than actually playing it, which is a shame.
I don't think there's a problem with the idea of "drawing bosses out of hiding." I'm worried that their execution is going to be extremely tedious and utterly boring to do though.
Even the idea itself isn't that good, imo. The repetitive nature of the progress structure is already boring in itself. It would be more interesting if different bosses had different gameplay loops involved with them. Maybe one of them was super confident and you need to do enough damage to get them to show themselves, another one you'd get closer to by working with, and then kill them when the time is right. Yet another boss could just have their own schedule throughout the city, and you could find and kill them at any place they could be at any given time, or even in between those places, on the streets. It would already make things more interesting than "do side stuff while you look at a damage meter to see how close you are to unlocking the meaningful content". Even if the side stuff is actually fun, it would get tiresome to go through the exact same process a bunch of times.