RMS power is something the audio industry seems to have dreamed up. There is no such thing as RMS power, but there is an RMS pseudo power which is the same as average power just called RMS power because you take the RMS voltage and multiply it by the RMS current.
What you end up with is the average power.
If we were to apply the definition of what RMS is to power directly, we would get some strange value that does not have any real use. The only possible meaning then must be Prms=Vrms*Irms, but calling it Prms is not really acceptable in circuit analysis it's the average power which results from a sine wave.