We had this same issue in our environment.
I noticed a crucial registry key for preserving icon locations was missing from the the default Windows Common Settings in UEM which we added (sounds like you found this too)
- 'HKCU\Software\Microsoft\Windows\Shell\BagMRU' (VMware KB2128007)
Once we applied that, it fixed 80% of our users, however, we still had a handful continuing to experience issues. What the heck Microsoft!?
After doing some registry comparisons, the key mentioned above was not behaving correctly on the problem profiles
- DWORD 'MRUListEX' had an unrecognizable entry
- BagMRU subkeys were nesting themselves instead of recreating top level
The Fix
Deleting the entire 'HKCU\Software\Microsoft\Windows\Shell\BagMRU' key completely fixed the issue. Once it was deleted, I logged out the user, logged them back in, and any desktop changes from that moment forward was retained every log in. Seems like an easy thing to automate for someone much more skilled than me .
What a pain!