I understand your position and argument. That it "10e-4" "is literally DEFINED as 10 x 10-4 ". Fortunately, it is not likely to be my problem at this late age. I rarely use the notation you mention, other than foolishly pasting it in from some other source. I would now not recommend it to anyone.
That authors of computer programs, and hence their followers, in failing to follow the rules for exponential notation set up over the last 100 yrs, court disaster, but what's new? Personally I recommend the use of the "^" symbol or the superscript equivalent, then no one will be left wondering why "-4" suddenly refers to one thousandth rather than a "ten thousandth". The leading "10" suggests to me that the base of exponentiation in that particular case is "ten" rather than 2 or "e" or some other base.
IMHO, the convention you are advocating is "way out" from intuitive, and could crash any laboratory exercise, or an important engineering effort . An order of magnitude is a lot of error to court because of poor attention to math notational fundamentals.
By the way, "e" has quite another meaning we surely all know. Borrowing that centuries old designation for "exponent" is yet another invitation to unintended blunder.