[analog31]

My understanding was that the "d" is an operator, and there are notations in which an operator on an operand is notated by just putting the one before the other. Also, the dx corresponds to delta x in the limit definition of the integral. One reason for keeping it, is that it makes the units of measure work out if the integral involves things that have units. So, notational consistency aside, it saved my arse when doing physics problems. ;-)

(even in my pure math classes, I sometimes imagined that the variables had units, to help find mistakes).

But your point is well taken about the consistency of math notation. Math spent most of its history being scribbled by hand and read by humans. It got the job done. And it was not uncommon to invent a new notation on the fly to replace an abstraction with a single symbol. That's the precursor to the subroutine.

The need for perfect formality of notation is a new thing, brought on by the computer age. This may illustrate the point that programming is not "just math," and math is not a form of programming.