For me it would be too exposed. To much dust, dirt, humidity and sunlight on the discs. Also hard to take with you. Hence I have them in a Systainer.

But if you go through them at a much higher rate in the same workshop; nice!

But you have a bunch with older hole pattern, so I wonder about your volume   

There was just enough room behind my chop station platform for a shelf to accommodate 5” discs in their original cartons.  I have sanding discs from 40 grit to 600 grit organized in sequence.

The top discs in each carton accumulate saw dust, but that cannot be harmful for a sanding disc.  By the time they are installed, most of the dust has fallen off.  I marked the cartons with bold markers as to the grit number.

It does require I walk about 10 feet from where I usually do my sanding operations, but the unused space is now used.  I’m pleased with it.

I buy my discs from Amazon in boxes of 100 discs.  Very economical, but the 100 discs last a long time.

I cut the lids off of the cartons for easier access. 

I keep a small vertical rack for dispensing a few discs at a time on my back bench. The bulk of the stock I keep is stored in the original boxes. They fit behind the Systainers on the pull-out. When the cubbies get low, I pull out a few more.
This is an old pic with no-hole paper for my pneumatic sander. I don't use it much anymore, so the shelves go refilled with the 9 hole variety. I labeled them with a Dymo machine too.
I don't have to be mobile, so that's not a concern, at least now. That may change at some point, then a Systainer will likely be the way to go.