Admittedly I've never tried to click this button except when the dialogue is waiting for input from me, but have just tried with some of my companions, and while the button takes a couple of seconds to appear when dialogue first initiates, I seem to be able to click it at any point even when someone is talking (and they continue talking behind the dialogue history screen). I'm sure you're right that things are different from what you've experienced before as it's not something I've played with much before except when I've clicked through too quickly and missed something, but I'm still not quite sure exactly what we are missing now that was there before or why it was useful when the current implementation isn't.
No need to explain to me of course, but I'm curious!