But in 2 we also have a stronger range than the raiser on most boards, don't we? (To be more concrete, maybe someone's stealing 50%+ on the button and our 3 bets are polarized, then our calling range is pretty strong).

"Initiative" isn't a reason for anything! I've seen it in lots of expert posts so I think it must be a code word for something I don't understand and everyone else does. The pre-flop action tells us what our range and their range are going to the flop, but aside from that it is in the past (from an equilibrium strat pov; obv it affects opp tendencies).

I'm guessing something like: "the difference between 1 and 2 is that in 1 our range is wider than theirs so we should be more aggressive and in 2 our range is narrower than theirs so we should be more passive"?