Holding water against the inside will not harm the tire itself, but might cause premature rusting of the rim if it is steel. The only reason I would have a cover at all is to protect from the sun. As McMonk says, if you don't want to continually clean, then invest in another cover that is mold/mildew resistant.
2003 Ford F-350 V-10 Crew Cab 4WD Long Bed
2004 Jayco Designer Medallion 29 RLTS 5th wheel
Bill, Gayle, and Mindi (dachshund)
Retired at last !
Nothing is foolproof to a sufficiently talented fool.