The sub crossover is a generic crossover, and you only get away with it, as it so low in frequency. It is a way less than ideal system.
Above 100 Hz or so, getting the crossover correct is crucial, and is in fact the heart of the speaker. An active crossover has to be designed with as much care as a passive one. The active crossover would not be in any way the equivalent of the passive one, as in an active speaker the drivers are directly connected to the amps, so there is no interaction between the inductive voice coil of the speaker and the conductive and reactive elements of a passive crossover. In the sub crossover situation the cross should be well below the crossover point to the mid or tweeter. Some speakers do have passive crossovers between 100 and 200 Hz, and these speakers to not work well with the receiver sub crossover arrangement.
We have three things going on:
1. The signal going to the speaker's terminals
2. What the speaker's crossover does with that signal
3. The signal that ultimately reaches the driver components
We know that in a standard, single amp configuration a full range signal is sent to the speaker, the internal crossover filters the signal appropriately for the different drivers, and that filtered signal moves the drivers.
In a passive bi-amp configuration, a full range signal goes to both the high & low terminals, the corresponding crossover does its filtering job and the filtered signal goes to the driver.
Using the
Paradigm Persona 5F as an example, the manufacturer nicely tells us some crossover information.
3rd order electro-acoustic at 2.4 kHz (tweeter/mid), 3rd order @ 450 Hz
Would there be any advantage to putting pre-amp filters on the signals going to the high & low sides - as long as they were in the ballpark? e.g. Just as bass management is used to filter out signals below 100Hz, have another filter that cuts out everything below 1000Hz for the tweeter side, and everything above 1000Hz for the woofer side? Those numbers don't need to be exact because the speaker's internal crossovers will still do their job, you just need to make sure there is enough signal that you don't cause a dip.
In theory, you would be making each crossover work less. Does it help if the tweeter crossover is not having to deal with 100Hz signal and only has to deal with 1000Hz & above signal?