I read a good argument in favour of senary on the basis of divisibility. It has nicer properties than base 12 for that. Personally for time I don't find the convenience of its divisibility to remotely outweigh the inconvenience for addition and subtraction of using a base different to the way we count.

Whatever base we use for counting, and I can imagine arguments for senary decimal duodecimal binary or trinary, we should use the same base for counting time.