Just to add to the discussion...active speakers don't specifically need to have integrated amps or DSP, is possible to design a speaker with an external, analog active crossover and leave the user with the amp choice (of course, if it is a 3 way, that's 3x amps).
The purest approach would be a speaker similar to the Sonus Faber Stradivari or ATC EL150, with a baffle wide enough to push BSC to room gain region (below 180-150hz aprox, this would require a 70-80cm width baffle, tilted back and, probably, positioning the speakers on the long wall of the room to get away without the +6db of Baffle Step Compensation) and using drivers with linear responses and equal sensitivity to avoid padding and EQ. In this configuration a true analog, active crossover such as Pass Labs XVR1/First Watt B4 can be used and of course, the user could choose the amps he/she wants (picture 3x Dartzeel or Vitus amps plus matching preamp there =D).
OTOH, if a magician starts building state of the art speaker drivers far ahead of what one can buy in 2019 at Madisound, another interesting approach arises, as drivers can be build with an intented acoustical roll off, ie: 18db natural roll off (this is what Raal does with their ribbon tweeters). This way, for a passive speaker, you can use just 1 cap and have a 1st order electrical but 4th order acoustical crossover filter. Assuming the speaker is like I described above (3 way, wide baffle to avoid BSC, tilted back for time alignment, drivers with equal sensitivity and linear FR + natural roll off on their intended pass bands), this theorical exercise would have just 4 crossover parts per speaker if made reality. This could be also done with the active filter (1st order electrical, 4th acoustical).
I believe that implementation is everything btw, and passive speakers have much less to go wrong than active ones, IMO the situation with active speakers and audiophiles it's a mix between market demands, misinformation, prejuices and the crude reality of having to buy your favorite amp x3+preamp, not having the option to use integrated amplifiers...yet on the other side of the coin the user not accepting the manufacturer supplied amps (which is very understandable in most cases, most active speakers use pretty sub par parts inside)...etc.