Of course the more the cleat interacts with other surfaces, the more it wears.
My experience with SPD-SL cleats is the "primary unclipping foot" wears down a bit quicker, although I usually replace both at the same time (partly for convenience, plus I find the yellow "walking grips" wearing out more evenly, so are worth replacing as a pair)
Similarly, the pedal on the primary-unclipping side will likely wear quicker - for example, after around 15,000km:
The SPD-SL pedals show wear nice and clearly; you can see I primarily unclip my left foot. The left pedal had significant vertical movement, and was overdue for replacement.
Is the action of inserting the cleat that damaging? or is it the standing on the right foot while waiting?
These will cause different kinds of wear, typically.. What is causing the wear should be pretty obviously if you look closely at how the cleat attaches to the pedal, or what contacts the ground when you stand (easily done if you take of the shoe, and clip in with your hands!)
For example, with the SPD-SL cleat:
The yellow bits (1.) will wear from standing, whereas the area that rubs (2.) will wear from unclipping.
Different types of cleats will be different, e.g the SPD "mountain biking" shoes have a recessed cleat, so standing will not wear the cleat.