They're all used for basic navigation.
You'll find the most written about the cycle of fourths/fifths because that has so many uses: identifying key signatures, modulating by secondary dominants, identifying the I-IV-V chords in any key, quartal/qunital harmony etc.
The others aren't done as a circle, because the relationships are different. The cycle of fourths/fifths applies to all major/minor tonalities within a 12-tone system. Every major or minor key has a perfect fourth and perfect fifth in the scale; following fourths or fifths gives you every single key within one structure.
Other intervals don't give you a complete circle. Using major seconds returns to the same root, but leaves out half the keys... you'll find this is true for the other relationships as well - your tritone sub chart isn't a circle; it's six separate relationships, becasue going up a tritone from C gives you Gb, and going up a tritone from Gb gets you C again.
So instead of using 'cycles', people just learn the spellings of the scales and adjust; if you know what the fourth and fifth notes are in the scale, you know the tritone falls between them.
The other intervals that have really wide use are:
Thirds (major and minor) and sixths (major and minor) - widely used for harmonizing parts. There's no true cycle here, as each key is a mix of major and minor thirds/sixths. They're learned by learning scale spellings.
Major seconds - these create the whole tone scale; there are two 'cycles' needed to cover all keys. Other than whole tone scales, their only real use is in secundal harmony.
Minor seconds - also used in secundal harmony. There's a simple name for this 'cycle' (which is the only complete one other than fourths/fifths): the chromatic scale. Playing minor seconds in harmony gives you 'tone clusters'
Minor thirds - these fall neatly into the diminished scale. They work well over diminished chords or dominant chords (since the upper three notes of a dominant chord form a diminished triad, you could use the series of minor thirds beginning a half step above your root) There are three 'cycles' of minor thirds.
Major thirds - the major third 'cycle' returns to the root after three notes (C-E-G#-C), so there are four 'cycles'. These are the augmented chords.
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