How is that precisely? I'm not as well versed as you. How would you explain this to the layman?
I have been busy getting ready for England, and leave today. I have been think how to reply to your question. In addition I have never owned or serviced an amp with Triple Darlington output stage, so I have had to become more familiar.
In order to get decent power out of an amp the output stage is divided, and one half produces the +ve deflection the other the -ve. So in many ways it is a flip fop switch. The commonest arrangement is the quasi complimentary compound pair, the Darlington pair next and fully complimentary compound the least common.
The Darlington is attractive because the output transistors are all PNP or all NPN. In the other arrangements you have the problem of matching PNP and NPN output devices. In addition providing higher current to low impedance loads, with less heat dissipation is also attractive.
Now to increase power you can parallel devices. For instance the Quad 303, 606 and 909 use triples, but the arrangement is such that the six transistors act effectively as one quasi complimentary compound pair.
In classic triple Darlington the transistors are cascaded. This I have found is where the problem arises, as there is delay with frequency between the switching of base to emitter. This results in time smear.
There are a lot of variations on this topology, with Bryston using a novel triple Darlington topology and Nelson Pass has designed with triple Darlington.
I have no idea if the Niles is classic Darlington or not. However Niles are not known as an amp manufacturer particularly.
So classic Darlington triple has phase shift or time smear, if you will, with increasing frequency.
Having said that the vast majority of loudspeakers are totally awash in phase and time anomalies.
Just to be clear, I now see the Bryston paper on Darlington was R & D. All their production output stages have been of the quasi complimentary variety, which they concluded was the best arrangement.