I'd say that the representation of numbers is an important part of math.
That said, I'd agree that decimal is not a particularly interesting part of math. For reals, continued fractions are probably the most interesting representation, and have nicer mathematical properties, at that.
To the extent that 'regular' mathematicians pay attention to these things (which a good number do), I don't think it's because decimal representations are inherently that interesting, but more because some of the number-theoretic and meta-mathematical questions are interesting and yet a bit puzzling. We don't yet really have a great handle on proof techniques and understanding of these kinds of problems: why should some simple-to-state claims about integers and iterated operations on them be true, and others false, and why are some seemingly true ones so hard to prove (like the Collatz conjecture)? The fact that this one is about rearranging digits in base-10 integers is just an intuitively-appealing way of stating simple properties, but the interesting thing isn't really about the base-10-ness imo.
That said, I'd agree that decimal is not a particularly interesting part of math. For reals, continued fractions are probably the most interesting representation, and have nicer mathematical properties, at that.