I made this rack many years ago and have been using it ever since.
We have high humidity in Florida but as long as the rolls are covered they seem to do fine. I keep the lid closed.
The room is air-conditioned, and heated, so that probably helps.
I store other rolls not being used immediately in plastic in their boxes on a shelf.
Rolls I plan to use soon get stored on the racks below the lidded box.
Every part of the world is different with climate conditions and it also depends on how hygroscopic the substrate is.
I think mainly keeping dust off, and keeping the room climate controlled, thinks go well for semi-open storage.
Mark