Reasons

Of the links mentioned, the Philharmonic Audio page is the only one that accurately describes how a TL works. The first article linked is full of inaccuracies and just plain wrong information, the fact it was written in 2016 is very surprising.

There have been four different pieces of software available over the past 20 years that accurately model TLs.

1. Augspurger's TL program which I do not believe is still available.
2. My MathCad worksheets which are no longer available.
3. Hornresp
4. Leonard Audio TL progrma avaialble on DIYaudio.

If you want more in depth information on how TLs work and can be designed look at the TL page on my site.

www.quarter-wave.com

Martin

@sound22card- My post was intended to(directly and concisely) address your questions. Hopefully, that was accomplished, despite my having misspelled, "Thiele/Small".

(MJK) Some answers.

What are the attempted advantages of a TL speaker cabinet with equal sizes channels all the way to the port, as opposed to each channel being wider than the last?
(MJK) A constant area TL with need to be L = c / (4 x f) long to produce a fundamental 1/4 wave mode that is tuned near the driver's fs value. There will be higher harmonics generated at 3 x fs, 5 x fs, 7 x fs, and so on. You can mitigate the peaks and dips in the response by offsetting the driver 1/5 to 1/3 of the TL length and by adding stuffing to the first 2/3rds of the length.
The worst ripple and most ragged response will be achieved with a TL that expands from the closed end to the open end. The open end will never be large enough to be a horn loading so the standing waves will be very strong. To achieve a fundamental tuning frequency near the driver's fs the length will be much greater than L = c / (4 x fs). The harmonic's (3/4, 5/4, 7/4, ...) standing waves will be closely spaced just above the tuning frequency. This is a very difficult design to tame and get a decent SPL response. I would not recommend this style of TL.

Also, what is being achieved by a decreasing size horn channel compared to an increasing size channel?
(MJK) My recommendation is to use a severely tapered TL with a closed end to open end area ratio of at least 10:1 if not higher. This will produce a shorter and smaller TL compared to a TL with a constant or expanding area along the length. You can taper the line in steps of decreasing area or a constant slope. A simple single fold TL will work well so all you need is a slanted dividing wall in the enclosure.
A decreasing area TL will reduce the required length for a given tuning frequency. The length will be much less than L = c / (4 x fs). It will also push the higher harmonic's (3/4, 5/4, 7/4, ...) standing waves much higher in frequency where the stuffing is better at damping the peaks and reducing the resulting ripple. Mount the driver at 1/5 of the length and stuff the first 2/3rds of the TL with fiber.

Are there any simple answers to these questions? I probably won’t comprehend a high level answer.
(MJK) No simple answers. TLs are difficult to design and get an optimum result. An accurate computer model to simulate the TL and iterate the design is a requirement to get it right. Rules of thumb and other commonly accepted myths for TL design will produce a hit of or miss result, you would need to be very lucky.

Thanks for the education, people.  I don't underestimate its value.