Power gain of amplifier
Several good reasons for using Decibels (or logarithmic ratios for measurements) are:
Dynamic range-using logarithms caters for the potentially large ranges e.g. of gains in electronics. 30 Decibels is a 1000x increase in a quantity.
The gain of isolated circuits can be evaluated simply by adding their gains in dB (multiplicative property of logarithms).
Quantities that decrease or increase rapidly are represented by linear changes in the logarithmic domain e.g. simple first-order network such as a RC circuit will have a roll-off of 20 dB/decade.
You are correct that it is just a convention but it has useful properties.