There’s nothing particularly convenient about base-ten; for real-world uses base-twelve would be preferable thanks to its large number of divisors (and even larger number of divisors of its multiples like 60). Which is exactly why 12 and 60 historically appear in many contexts.

A number theorist would probably want a prime base, so that N (mod 10) would be a field.

A power-of-two base wouldn’t be particularly convenient to anyone except a small minority consisting mostly of hardware and software engineers.