I don't love the $...$ syntax for executing commands. Using $ as a string delimiter is very strange to my bash-accustomed eyes. It's a shame that they provided such weird syntax for the most important thing you tend to do in a bash script, while providing fairly nice syntax for everything else.
and i dont like how it's inconsistent that echo is not using the $ syntax (which makes sense internally, as it's a built-in, rather than executing the $echo command). Overall, it is cute and neat, but i find that if you are looking to write bash scripts that require this level of programming, you'd be better off writing it in python, or perl. Only in very austere environments can this be utilized, but the requirement…
I don't remember ever installing bc, but I use it frequently and it's always there. Are you sure it's not already part of most base systems?