I believe the OP has a 40 gallon, which is not large enough to sustain Tw grazing habits of a mandarin, unless he could get it on prepared foods. That's really hit or miss. Any of the smaller wrasses will eat pods, as will most small fish. A mandarin would eat every last one in a few days, then begin to starve. Copepods provide live food, enrichment for the fish (hunting behavior breaks monotony), clean up waste, and increase the overall biodiversity. There are no substantial drawback that I know of. Visual appeal is very subjective, but once you know something is good, it becomes a lot easier to see it all the time.
If you want fewer pods, just feed less. But be aware that half the saltwater people on here would give their left leg to have that many pods in their tanks.