There are multiple levels on which one could answer this question.
For one thing: 1, 5, 7 and 11 are the only* numbers coprime to 12, hence the only way to traverse the entire 12-edo palette through iteration of a single interval is with fourths/fifths or chromatically.
The sequence you ask about is in essence descending in whole steps – this obviously does not cover all 12 keys; the remaining are simply “filled in”, by immediately repeating each key a half-step higher. If you allow for such combinations, there are of course much more possibilities to traverse the palette.
Now, set theory actually has nothing to do with harmony. Really, the reason fourths and fifths are the most common modulation intervals is completely unrelated to the above argument: these intervals have the simplest frequency ratio, namely 3:2 and 4:3. Hence notes from both keys share a lot of overtones when played on most† instruments. This is why keys spaced by a fifth “sound related”, allowing modulations to go very smooth and natural.
(It is actually a pretty beautiful fact about the 12-edo tuning system that the most harmonic modulations are the only nontrivial ones that reach every key!)
Clearly, 3:2 and 4:3 are not the only nice frequency ratios. 5:3, 5:4 and 6:5 would be the next best ones. These are the just-intonation major sixth, major and minor thirds. They have representations in 12-edo tuning, albeit unlike fourths and fifths (which are virtually indistinguishable from just intonation) not quite exact. In fact the 12-edo major third is right between‡ a just-intonation (Ptolemaian) 5:4 and the stacking of two Pythagorean whole steps. This creates a sort of ambiguity: a third can be heard both as an “atomic” consonant interval, and as a compound scale degree. I'd speculate that a full modulation§ over one of these intervals is rather perceived as compound and hence doesn't feel nearly as natural as a fourth/fifth modulation. That does of course not mean you can't modulate by such an interval, only, it will have a much starker effect as a fourth/fifth modulation.
I find it very interesting how these facts would translate to different equal-tempered tuning systems. In particular, in Bohlen-Pierce like systems, 5:3 takes the role of the most natural modulation interval. We definitely need more music in such systems to properly explore these effects!
*The only 12-coprime numbers that are themselves smaller than 12. IOW, the only coprimes modulo 12, that is, up to octave shifts, which are usually considered as irrelevant for such matters.
†Amongst the notable exceptions are gamelan instruments, which match harmony systems completely different from our Pythagorean/Ptolemaian derived ones.
‡Because 12-edo is a meantone tuning.
§But also consider modulation to a relative key, which is very natural! Only, it can't really be iterated.