Single way or multiway

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.  

as a dealer for over 30 years our perspective our this question is simple

we have never experienced a single driver speaker worth owning the reason is simple you need a proper high frequency driver to produce clean and airy high frequencies and in the history of audio we have been moving into better and better tweeters from paper to plastics to metal domes to damped metal to ribbons and AMTs 

as long as the tweeter is well matched with a properly implemented  crossover you can create a seamless totally transparent music reproducer 

Dave and Troy

audio intellect NJ