Single way or multiway

The design concept (single driver, multiple driver/planar, horn, dynamic, etc.) is not important.  It is the execution of the design concept in the design control, design transfer, and manufacturing process that is critical to sound quality.  Each design concept will have unique characteristics, strengths, and weaknesses which we may be more or less sensitive to.  For example, I have never warmed up to the sound of any single driver speaker I have heard, but do acknowledge their exceptional coherence through the range they reproduce.  I have heard multi driver speakers where I hear each driver’s characteristic (not a good thing) and others that are as coherent as single driver speakers, but extending further in both ends of the frequency spectrum.   The conclusion, there is no right or wrong.  It depends on execution of the design intent and our personal sound quality preferences.  

I suppose most don't fret about their passive crossovers since the loudspeakers they've chosen provide contentment. The importance of knowing the specs of one's speakers and providing sympathetic amplification mitigates most issues. I've not seen empirical evidence that provides universal superiority of minimalist passive or active crossovers vs more complex crossovers. Speaker designers  are pretty sophisticated these days, have many drivers, crossover components to choose from, based on listeners experience I trust they know what they're doing. If what you propose is clearly superior don't you think they'd go down this path?

Bache, not sure what you are trying to achieve with this post. As A manufacturer, I would normally assume that you would try to achieve a broadband reasonably flat curve doing little harm as possible to phasing... Not the case? I also look at keeping impedance swings flat as possible. In crossovers, I do prefer to keep part counts down, but if a 3rd or 4th order is needed for driver protection or to preserve phasing, then yes, I would use higher orders. I can only guess that the 10th order slopes that you quote are trying to achieve a brick wall effect to have an absolute start & stop frequency. I hope that you would know those benefits. I've tried very steep slopes and always preferred standard 6 to 24 DB slopes. However, well done brick slopes in active crossovers can be great. 

I grew up using speakers that were no more than 8” full range drivers with wizzer cones attached.  Then I bought some ADS 300’s. Tiny two way speakers with a big sound. Then came my first subwoofer and a separate active crossover to fill in the bottom.  Essentially making my system a three way. Much later came the DQ-10’s with their 5 way crossovers.  When I added the sub and crossover it became a 6 way speaker system. Now,  I have a 3.5 way and a sub. 
I bet the crossover’s in the Amati’s cost more than my first few systems combined!

I sure have come a long way in my journey.

One of the leading proponents of a single full range speaker element with no crossover are Pearl Acoustics and Mark Audio.  Both keep the driver fairly small to preserve some high frequency dispersion and so give up deepest bass extension. 

Fritz, Totem, and maybe others have made 2-ways with "capacitorless series crossovers" to closely approach the ideal of a full range driver without the loss of high frequency extension and dispersion.  

The EPI 100 and all its siblings used a single cap to attenuate lows to the inverted 1" paper dome...couldn't be simpler!

The Walsh driver found in the Ohm A, F, and more recently German Physics' DDD driver, which to my knowledge use no crossover components, yet achieve full range and omnidirectional coverage.

The Infinite Slope and Gauder approach is the other end of the spectrum.