But db(A) doesn't really measure that for anything but sounds that could cause hearing damage, or test tones. You've essentially taken a newcomer's problem of underspecification and carried it into the given domain.
I feel like it'd be better to say dB(A) measures flaunkis, which is defined by the human frequency response. Then the newcomer's next question will be something like, "how do I use flaunkis to compute the loudness of a music recording?" And that's the right question to ask, because the answer is: it's complicated. :)
The people who get confused by decibels, are exposed to other people treating it like it's a unit in its own right.
I agree that what the parent described, should be done. If it was what was done, this article wouldn't exist.
Right now what we've got is basically "millis", and you just have to know whether the speaker is talking about length or mass. I like your proposal.
There are filters we measure on power, there are filters we measure on signal amplitude, and "signal amplitude" can be ambiguous on some contexts too. There should be a way to specify this one better.
Some Scientists and Mathematicians would rather use random log_10(x) functions than allow units like km/km in their formulas. It's wild, and SI has been a part of those decisions all along.
Nobody (I hope) says that 100mW is "10 dBm" more than 10mW. That would be wrong. Readers would be confused. Most people would cross their fingers and correct it to "10 dB", but who knows what it might mean?