What mijostyn said about group delays and time delays is correct. It was discovered in the 1930's, by MGM studio.

Below article from The Klipsch Audio Community:

This entire thing goes back to the Eleanor Powell "double tap" incident at MGM studios in the early 1930s. When monitoring playback of Powell tapdancing an echo was noticed on the taps. John Hilliard, subsequently the greatest of all horn designers, was a young sound engineer at MGM and traced the problem to the 8 foot difference in the path lengths of the horns in the 2-way Western Electric monitor speaker.

Hilliard did experiments that showed that the effect was time and frequency dependent and that a delay of less than 3 milliseconds (about 3 feet) was inaudible using crossovers between 350 to 800hz.

A result of this incident and WE's refusal to market their improved Fletcher loudspeaker was the decision of MGM sound honcho Douglas Shearer for MGM to design their own improved system which would among other things minimize time delay. Hilliard was put in charge of the project which then developed the famous Shearer Horn. An entire galaxy of talent worked on this system including Hilliard, James Lansing, Bob Stephens and even RCA's Harry Olson.

Note that though the folded bass horn of the Shearer cut time delay compared to the WE snail horns it didn't eliminate it totally but Hilliard's later Altec Voice of the Theatre did. So it seems that even though Hilliard thought some delay was inaudible the existence of any at all still nagged at him.

Which brings us back to the present day. Is the time offset of the big Ks a problem? Theoretically the distance falls under the distance Hilliard thinks was undetectable. Might it still be a problem? Perhaps. But keep in mind that all loudspeaker designs make compromises, given a choice, as PWK was with his design, between lower distortion and time delay which would you choose? I'd take the lower distortion of the horn system.

Photo of Shearer Horn from Lansing Heritage site

https://www.tnt-audio.com/casse/altec_a7_clones2_e.html
Isn't this thread really talking about a speaker design issue that is inherent in most if not all speakers: namely time coherence.  A couple of manufacturers address this issue by careful placement of the drivers and using first order crossovers. For example, .... Thiel, Vandersteen and Green Mountain audio.  

The late, great Roy Johnson of Green Mountain audio wrote some pretty impressive white papers on the subject.  Not sure if Roy's white papers are still available.

And DEQX sells a digital device that can correct for time delays in speakers.  I used to own a DEQX. The unit was inserted between my preamp and amp.  Although the DEQX added quite a bit to the SQ, I found, on balance, that there was a net subtraction because the DEQX added a lot of processing and manipulation to the signal. 

If there were more brick and mortar stores around that carried a lot more speakers brands, I would love to spend some time educating my ears to learn just how much better time coherent speakers sound as compared to those which are not time coherent.  John Rutan at Audio Connection, located in Verona, NJ, is a Vandy dealer and stalwart.  Perhaps John would let me burn some time one day in his shop.  

BIF      
There is also Enhanced Bass Alignment (EBA) developed by Meridian to address group delay.
@bifwynne buy a pair of full range single driver speakers and be amazed(I know I was) at perfect time coherence. My recommendation for something not to expensive is Audio Nirvana. 
That’s a remarkable measurement, didn’t know we didn’t know it.

3 things seem related

1. time alignment of frequencies, highs traveling a speck faster than lows. Some designers slope the face of their enclosures for this purpose. You can simply tilt/lean your flat faced speakers back to ’simply’ achieve that. It often directs the tweeters dispersion to your seated ear height, another benefit. Another benefit is the altered angle of reflections off room surfaces

2. cd players. most use a single DAC to process left/then right; left/then right ... I forget the speck of time delay this introduces, to EVERY l/r bit of conversion. To avoid this speck of time delay. better players provide separate L & R i.e. my first player, Onkyo had a matched pair of burr brown processors. Recent Oppo 105 has a pair of superior processors. I assumed, on that basis alone, the Oppo would beat my Sony Carousel. This (presumably) single processor Sony surprisingly sounds as good as both the Onkyo and Oppo. Thus, the l/r time difference of a single processor may be less than half a millisecond?

3. LP’s, analog. After nearly 50 years of attentive listening to Reel to Reel, 8 Tracks, Cassettes, home made cassettes made from LPs, LP’s, CDs and SACD:

My simple summation is that Analog ’Gets the Overtones Right’. Perfect time alignment to the fundamentals, perfect volume decay. Chopped Digital Re-construction is an amazing achievement, but many, my friends and I included find LP’s preferable to the CD version. I’ve cooked up ’somewhat blind, out of sight switching’ in the past, no matter what: everyone chooses LP over CD and Tube over SS.