It is safe to say that the longer the AMT, the lower the frequency the problems and transition towards line source behavior start. But I would not support the claim of ´more problems´ coming with length, as a long AMT might also shift the tipping point, i.e. the sudden transition from wide dispersion to narrowing one, towards lower frequencies, hence far away from horizontal dispersion problems, if we are talking about a rather narrow diaphragm shape.
The directivity imbalance between lower octaves and how they behave at shorter wavelengths, I would see this as the main reason why it is so difficult to handle AMTs. and with the standard sizes of 4...8cm in height and a ratio of less than 2:1 (height:width,) directivity problems tend to pyle up within one octave, and increase in directivity index is too sudden and overly steep. In my understanding the main reason why many AMTs sound bright in some concepts.
Personally I would say long and narrow AMT is easier to handle, if you deal with horizontal dispersion issues separately, for example designing a waveguide.
Guys from a German webshop offering DIY kits have been trying the 16cm AMT in such a concept:
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Sofia AMT12 is the name, maybe someone has listened to is and can tell you more. Definitely an unusual concept as the x-over freq supposedly cannot be brought lower than x2K, so I would expect the two midrange drivers being some 40cm away from each other, to do pretty interesting things. Bringing the two closer to each other with the help of a smaller AMT, in theory would reduce lobing and interference problems. On the other hand, you are more likely to have too much off-axis energy in the AMT´s lowest octave playing more or less alone. A phenomenon which is even slightly audible with the Finkteam Kim, employing the more forgiving 11cm version of this AMT and some pretty clever x-over design.
From directivity and compromise point, I guess a triple strategy works best on paper: countering the AMT´s uneven horizontal dispersion with the help of a waveguide, getting the x-over frequency to the lowest point possible, and doing something with the midrange drivers to keep the directivity constant at lower octaves. The latter is in my understanding a reason why MTM dipoles or midrange line arrays are such a good match with bigger AMTs. Their directitivity and subjective dynamic behavior is very much alike, and the virtual coax does add coherent imaging.