Phase Coherence or Time Alignment: Which More Imp?

How is it possible to build a phase-coherent speaker using 1st order filters?
I learned in electronics that a 1st order filter (ie 6dB slope) shifts the phase between woofer and tweeter by 90deg;a second order (12dB slope) by 180deg; third order (18dB) by 270 and a 4th order (24dB) one by 360deg.
This should mean that it is impossible to create phase-coherent first order systems, in a system using second order filters you'd have only to invert one driver to achieve coherence, a third order system again is impossible whilst a fourth order system is always in phase as it has been shifted by a full 360degrees.

Now, when it comes to to transient response and xover "ringing" ( electric resonance) a first order filter is unbeatable as the transient response is helped by having fewer passive components and the filters total inability to resonate. But for phase-coherency they are, together with 3rd order, the worst possible solution. You can fix 180 and 360 degree shifts, but theres nothing fixes 90 deg shifts, other than active electronics like in better bass-management systems for HT.

Thanks Roy,
indeed these difficulties can be minimized with careful design!
Thats why I use Tannoy LittleReds. It uses a combination of
first and second order filters. The phase response curve shows it to shift the entire audio spectrum uniformly by 30deg compared to amp output with a slight dip and a bump around the crossover frequency (+8deg,-10deg). So it acts as a time delay
(unavoidable) with a maximum phase shift of 18deg but this is limited to about 200hz either side of the x-over frequency ie the shift starts at 1k,
goes through zero (that is the 30deg total shift) at 1.2k rises again and is back at zero (30deg) at 1.4k.
Also, being point sources, they stay in phase no matter where you are in the room, unlike common multi-driver systems.

Personally, I have NEVER heard a speaker to be 'too analytical' or 'too revealing' although I heard speakers being 'too forward' or 'fatiguing' these usually featured metal-dome tweeters. I would have thought that 'analytical' and 'revealing' are essential attributes of any accurate speaker.
Without being 'analytical','revealing' and accurate any critical listening is
obviously impossible. People having problems with these attributes should probably by a Bose waveradio and just be happy with all the money they saved. They are the reason that high quality audio is in the dire state its in.
(Sorry, didn't mean to be ranting but statements like 'too analytical' just get me going. I am also aware that it wasn't you who said it, so don't take it personal.)
In my own experience, based on spending time in recording studios and listening to every speaker I can since I was 15 I have to say that Tannoys are closest to the real thing followed by decent studio monitors. Than come a variety of planars ( fantastic at low volume but lacking in macro dynamics),
full-range drivers ( great dynamics and imaging, bad at low volume, dodgy treble and (if in a horn) lumpy bass response.
After that the majority of dynamic speakers who do everything somewhere between average and badly.

This, of course, is a grotesque over-generalization as there are really bad studio monitors and really good HiFi speakers. I have not come across any
green mountain gear here in Europe so I cannot say anything to your product.
Overall you still have to look at the whole speaker-system and not just the xover, my Tannoys have loworder filters and sound fantastic, most studio monitors use fourth order and sound very good and back in the 80' I came across some 5way, first order filtered Dynaudios which also were excellent!

Cheers Golix
(haven't founded anything but...
can explain gravity without
bending space)