Power planes were very popular back in the 1980's for digital designers. They thought that the power plane made one big capacitor, and that somehow helped with digital crosstalk. What really was going on is that they did not have a clue. As the digital electronics moved up in clock rate, the power plane became a good way to CAUSE digital crosstalk and supply glitches.
I suppose there might be low frequency applications where there is a good reason for one, but I can not think of one off the top of my head.
If you want high capacitance between your power supply line and the ground plane, try a chip capacitor.
In RF I seldom use them because most of my circuits require lowpass filtering in the various DC supply lines. This is to either keep spurious signals from re-entering a signal path, or to keep EMI radiation to a minimum for communications circuits. If you have a "power plane", it is had to drop a couple of ferrite beads along the way to de-Q the bias lines!
Jeez, power planes! I have enough trouble trying to keep the
ground plane EMI free!
Rich
www.MaguffinMicrowave.com