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ABX has a flaw, I agree.

I agree that ABX has a flaw.
The flaw is that amature statisticians use a chi-square or S-T test to compare the results without an understanding of "Power of Study."
Power of Study, briefly is a mathematical estimation of how many trials will be necessary to expect a statistically significant result.
The variation of results is high in audio testing. If you ran an ABX where X is always A, you would get some variation in responses. If the variation within the groups is almost as high as the difference between groups, then you will need to do a very high amount of tests to separate the noise of the test from the data. That would be quite tedious - so it is probably not reasonable.
I haven't calculated a Power of Study since residency, but I would not be surprized if most differences we are talking about would require 1000 loudness matched X's.
There are things that should minimize the noise: Experience of the listener, hearing acuity of the listener, familiarity with the music played, etc.

I am curious to know why you have not liked the ABX.

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