Within DnD 5E, the number 20 is a central motif of system design. The basic roll is made on a d20. Ability scores cap (or at Peak at) the number 20. The level cap is 20. Potentially this could be coincidence; it is also possible that it was an aesthetic choice. It concerns me, however, whether diverting from this symmetry would have any measurable consequences to play itself.
Is there a mathematical consequence to the symmetry of these design elements?
Knowing this would help determine both the reason for this system and whether altering it would have a serious effect on the math, but the question is more concerned with the math itself, rather than cause or effect. The answer could of course be 'No, there is no mechanical reason for this,' but I'm seeking a reasonable investigation into whether or not any sources indicate that this occurrence exists with design-specific implications. I'm curious if I'm missing something- perhaps some rule which makes use of ratios between these aspects of the game; ratios which, of course would need to be adjusted if these scaled differently.