If I were writing this, I'd play up the concept of a "pocket" dimension. So, maybe they were made with the intention of recreating the "Handy Haversack" trope, but something went wrong along with the way— like you said, reaching in, no one can be sure they will pull out the item they left (or that they will ever even see that item again).
It's an actual infinite space, meaning that it's probably larger than the actual universe. Things drift. Things get lost. There's debris in there the makers never put in, now. Maybe there's star systems in there somewhere. Maybe there's intelligent life. Maybe there's nothing, forever.
So maybe it's possible to use it as a "Handy Haversack" for a little while, before things start to shake away and leave. Or maybe you pull them out and there's something just wrong with them, like they aren't playing by the right rules anymore.
TL;DR: I'd go the 'wanted to cheat girl pockets, accidentally made a universe in seven days' route.