It just makes sense to clean them all at once.
It will prevent one of them from being forgotten and becoming a bed of disease.
The mess of cleaning will happen once, not again and again for every feeder you clean.
Bird feeders can spread salmonella among other diseases so it is important to protect your home as well as preventing the spread of disease among our feathered friends.
And one of the best ways to do this is to do the job outside.
(If you have a lot of feeders and cleaning all of them in one day would be too big of a task, then do some one day and the rest another day.)
Sit back and enjoy the sights and sounds of healthy, happy wild birds at your clean feeders!