> If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)

This is the part I don't get. This is the part where "dB is just a multiplier" falls short. It's there to "so that the related power and root-power levels change by the same value in linear systems" (that's how Wikipedia formulates it). Why is that even something you would want? Isn't it much more logical, intuitive, consistent and useful to reflect the fact of power being proportional to the square of the signal in it having double the dB value?