Does part active speakers waste amplifier signal quality in process of filtering

[Objectivist01]

I m always skeptical in introducing a speaker level subwoofer in to a system. Always I feel that the signal from the amp when Partly used up by the high to low converter of the active subwoofer looses strength before it reaches the passive part of the speaker. For example Martin Logan is a speaker which essentially like a ls 50 (passive) with a pair of active subwoofers connected with speaker level input.

Are we wasting the quality of the signal from the amp this way?