Actually it does. On macOS is you grab a program from the internet that doesn't have a valid developer signature it won't run. You can of course authorise that file to run (it requires admin privs) which sets an extended file attribute which doesn't exist in NTFS or FAT32 or ExFAT. If you copy that program into one of those filesystems then copy it back it'll have lost the authorised flag and will be blocked again and require admin to re-enable it.
That's the edgiest of edge cases. Not something that most users would encounter.
This is exactly what you would need to do but depending on the complexity of the filesystem, writing the export and import tools to capture all the data disassociated data structures and metadata and archive it is not trivial. Especially, as I mentioned above, ideally you'd at least want those stored games to be kept up to date with the latest patches meaning your virtualised game image also needs to be able to grow. Now you're basically writing an entire virtualised filesystem for a f***king games console!
That's adding a level of complexity that doesn't need to be there. The game can be updated after it gets thawed. Still much better than having to redownload or re-install from disk (and then update).