Yes, I see the need for a phasing plug for a 40Hz bass horn. Most people choose to ignore the finer details and claim the wavelengths involved are too long to be affected by phase plug. If someone really understands the fundamentals of sound origin, then a phasing plug begins to make sense.
All you have to look at is Fourier transform. All “natural” sound consists of fundamental and harmonics. If a speaker does not reproduce the harmonics correctly, then the tone is not reproduced correctly. It is the harmonics at the higher frequencies that help shape tone.
You can take a sine wave and make a square wave by taking the fundamental and adding together its harmonics. If these harmonics are not added together correctly, then you cannot reproduce the sound. Think about what will happen to the music you play if your speakers did not reproduce the harmonics correctly. The waveform would not look like the original and it will not sound true.
Low E string on a bass guitar has fundamental frequency of 41Hz. However, its 2nd and 3rd harmonics have much higher amplitudes. This is normal behavior for a lot of musical instruments. It is very common for the harmonics to have higher amplitude than the fundamental note being played. Below is the frequency response of a guitar. You can see the fundamental being played is centered at about 65Hz, however the harmonics have much more amplitude. The relationship of the harmonics to the fundamental, and the other harmonics are responsible for the tone of the instrument.
So, even if you cutoff the bass horn at 160Hz – 200Hz, it still must get these higher frequency harmonics correct for 40Hz to be reproduced correctly. The real trouble begins when you must have the mid bass horn handle the harmonics of the fundamentals coming out of the bass horn due to the crossover point. You have to get the fundamental coming from the bass horn to sum correctly with the harmonics coming out of the mid bass horn. This is very tricky to get right.