First, the practice of assigning opus numbers was not very common in
Mozart's times.  Only a handful of Mozart's works have opus numbers.

Second, Mozart is not really very special in this respect.  There is
practically no major or semi-major composer whose works haven't been
by now catalogued and in most cases assigned a catalog number.  Mozart's
cataloguer was L.  A.  von Koechel, that's why you see a "K".  The reasons
that using "K" is so common are:  1) there are so many of his works of the
same genre and key that some way of distinguishing one from another is
needed; 2) the Koechel catalog was probably the first scholarly catalog
(in the modern sense) of works of any composer; 3) Koechel's numbering
has been in common use for the last 160 years, and people got used to it.

Bach's works are nowadays preceded by "BWV", for instance; Haydn's by "Hob".

-Margaret