Different guitarists use different diameter strings because the diameter determines the tension when you tune to pitch. Different people prefer different tension. Most shredders prefer light tension. Most jazz players prefer high tension.
The diameter is compensated at the bridge and in some guitars the nut. When you press a thin string to a fret, the center of the string is closer to the fret than when a thick string is pushed to the fret. Thicker strings compensate for this by using slightly longer length which you can adjust at the bridge.
One type of non parallel frets are called true temperament frets. They are sort of parallel but squiggly. This results in better intonation closer to that of a piano.
Another type of non parallel frets is multi scale or fanned frets. This allows the bass strings to have a longer scale length, which allows you to use relatively thinner strings for bass notes. This is important because when strings get thicker relative to their length, they start to behave more like cylinders with thickness rather than ideal springs, and sound rather nasty because harmonic overtones are out of tune with the fundamental.