I've tried it both ways for years on various riders and now I leave um off (UNLESS they are in a place where you might catch your foot etc in the pulley).
I haven't noticed any difference in performance with either method, it's just that I clean them more regularly when the covers are off.
I think I'll leave them off for awhile. One is completely under the deck and the other only sticks out about 1/4 of the pulley.
My 42" Craftsman Tractor doesn't have them, only the Zero Turn.
My blades stop when I stand up anyway.
If you have an electric PTO then the belt covers can be left off they are just a safety device to prevent finger & feet getting caught in the belts .
If it has a manual PTO then some covers also double as belt keepers.
On my covers I drilled Two 1/2" holes into each cover, just below the pulleys. When blowing mine off I use my leaf blower & aim it up the holes. They stay clean now.
PS: Just my .02 I NEVER use any water on mine, blow it off with air & give it a wipe with a California duster. Done.
Too many electrical connections & spraying cool water onto hot spindles, is not something I will do.