4th order crossovers: design and time/phase issues

I have noticed some companies use 4th order crossovers...while others use 3rd, 2nd, and first...what are the advantages/disadvantages of such a crossover network...I have seen them mainly utilized on the mid-bass driver..is it possible to achieve true time/phase consistency with such a design?
This is a point of contention from most manufacturers.
THIEL uses first order, stating that this is the only true phase correct design. Several others agree.
Those who disagree, claim that first order is only correct at the launch point of the drivers, and that lobing caused by commonly shared frequencies of the multiple drivers, cause drastic frequency shift at points within the listening room.
I personally take the position that a great designer will use whichever crossover works best in a given speaker, and with each particular crossover and driver within that design. That may mean first, second, fourth etc. It may seem obvious that some designers have 'painted' themselves into a technology stalemate by adopting one technology, hanging their reputation on it, and then being forced to use it com hell or high water.
The only thing certain in loudspeaker design is variables.
So to my way of thinking, a great designer should be flexible, not dogmatic.
Then you have the series crossovers/parallel crossovers factions. Google Bud Fried or series crossover for more.
At the risk of taking the flamers to the kindling point,the lack of a crossover is why the Magnepan MMG is,in some respects,better than the 1.6.