I guess I'm mostly trying to understand what benefit there is, if any, to running a higher order network on a speaker that is already phase and time compliant with relatively low intermodulation, unless you're using drivers that are wildly out of spec.
Out of spec drivers are not the issue with crossover order; 1st order/6dB, 2nd order/12dB, 3rd order/18dB, 4th order/24dB, etc.
In a very general sense, if you have wide bandwidth drivers and they can handle moderate to high power, you can probably use a 1st order/6dB type crossover and have good sonic results from the speaker system.
In a lot of cases, you use different crossover topologies in the same crossover network like the "universal". The woofer section of the universal is 6dB low pass, the midrange section has a 6dB high pass & 12dB low pass, the tweeter is an 18dB high pass.
Low(er) order crossovers also save money. Crossover components can easily add up very quickly adding significantly to the manufacturing cost of a speaker system.
Again, in a very general sense, if a speaker has good performance over a limited bandwidth, you can use a higher order crossover to utilize the bandwidth area of importance and filter out the anomalies.
One advantage of the "universal crossover" is the fact that it has an almost constant impedance across the audio band (except for the main woofer driver resonant peak) because I use a lot of SE amps with no feedback and it helps tremendously to have a flat impedance curve with these type amps.