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.
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.
It would make way more sense to use J and J/h instead