Just putting my thought out: aren't passive capacitors and coils (C an L), and maybe even resistors causing a PHASE shift on passive crossovers, and NOT so using active crossovers?
In my mind, the question is active vs passive CROSSOVER.
40 years ago, we built our own active crossovers (and tri amped our Electro Voice (I think it was called a Sentry 3?) and made it sound great even on classic music). I know bought (still in box) a miniDSP 4x2HD with hopes it can provide a 2 or 3 way active crossover (to drive my Infinity Quantum 2 with seperate amps for the Watkin bass, mide cone and dome tweeter/EMIT tweeter (maybe tube amp?).