Hi Mister Rogers,
Taking a quote from the movie “Steel Magnolias”…”The ability to accessorize is what separates us from the monkeys.”
Many of us will accessorize our milsurps with stuff like bayonets, slings, muzzle covers, etc.
P0H0 has chosen to accessorize some of his collection with breech/action covers. A quick search of previous post, concerning breech covers, will reveal much. IMHO, I believe having the covers on will not damage the firearm if maintained in an environment where the circulation, temperature and humidity are properly controlled. However, as general rule, many will not store their firearm collectibles with accessories attached to prevent possible undue damage, wear and tear or rust.