I've found "1e&a2e&a3e&a4e&a" notation is often used to describe ballroom step timing, but I've not found any authoritative source for it. It even looks like a recent invention for the Internet era. So my question is, is it really widely used and unambiguously understood? Are there thorough instructions for using it?
At least in the US, this notation is very commonly used for counting rhythm. In fact, in my experience it's the most common method, but that's just based off of first-hand, anecdotal evidence.
But although this notation for sixteenth notes is pretty standard, notation for other subdivisions varies much more. For triplets I've seen "one trip-let," "two la-li," "three ki-da," and so on. Although your sixteenth-note notation doesn't need any clarification, you may find yourself having to clarify your notation for note values of a triplet and smaller.
It's not recent, I'm in my 50's and when I started taking piano lessons (I still play!) that's how 16th notes were counted!