It doesn't. Watts were a mistake by whatever committee it was that standardized unit names. Power should not have been given a unit; it should have been left as ∆energy/time just as velocity is distance/time.
Joule is a derived unit, it is kg*m^2/s^2. There are lots of derived units, like hertz and newton, because they useful than writing out the whole thing. Electronics would be really annoying if had to write out volt, ohm, and watts (ampere is base unit, coulomb is derived).
Don’t put words in my mouth. I only said that power should be J/s instead of watts. The “per second” part of that is what is most important thing about power. It’s the rate at which energy is accumulating or being used up.
Using watts is fine for anyone who deals with energy and power all the time. The problem comes when the lay person tries to reason about power. If power were written as J/s then they could use the same reasoning that they are already familiar with from dealing with speed and position, or with flow rate and volume.
I regard that as a downstream effect of giving power a unit in the first place, but yes. We should have just stuck to J and J/s. It would have prevented the kWh and also abominations like the mAh “capacity” ratings you see on batteries.