It's not a case of mathematical purity, it's a case of unnecessary ambiguities. Decibels would be a heck of a lot more comprehensible if a) it was always a ratio or an absolute value with respect to an explicitly written unit, and b) it was always in that unit and not sometimes scaled differently because it's power instead of amplitude, and it would be no less useful to you for exactly the case you're talking about. (RF at least generally does say 'dBm' when talking about absolute power, but it would probably be better to way dBmW, and we could also use dbmV where it made sense without having to go 'oh, but that's divide by 20 just because').

Of course, it's far too late to easily change it now, but it doesn't make the current situation optimal.