Is there any significance to numerology being base 10, using numbers 0-9?
Why can't we use binary, base 12, hexadecimal (base 16) or some other system?

have you ever watched the tv series  (numbers)

Seen NUMB3RS, but can't really follow it.  Is this relevant to the topic at hand?

yes it is, the story line is based on a mathematician making predictions  using numbers and formulas

i have yet to see a personal reading done with the use of higher forms of math :calculus ect , but if you look deeper into numerology as it is known  you will find that your basic algebra, geometry are used in basic elementary forms  astrology is another example ...   as for as number based systems: binary  , base 12, hexadecimal (base 16) or some other system  again these principles  are in place in crude forms  .   the systems in place now, to do readings work with  a high degree of accuracy i personally dont see the need to include different number systems   can you imagine views  a personal chart using the binary system  nothing but 010101010100011010100