Your theory would work if all signals, including those internal to the opamp, are limited in frequency.
Most "DC" applications have edge case transients (minimally, power-up) that matter, too.
With slow opamps (say, GBW significantly below 1MHz) you may be able to get away without power decoupling. Does it make sense, though? But thinking about it and questioning is a good idea.
This also depends on your power distribution network. Power is coming from somewhere and that somewhere typically has output capacitance already. How long and what shape is the wiring?