So I decided to add users to the Backup Operators group to all computers in the Domain by editing the default domain policy and adding a restricted group. I also set the Volume Shadow copy to start as part of the default domain policy as well.
One of these two changes seems to have made it so Volume shadow copy will no longer start on any computers in the domain.
I tried undoing both these changes, force pushing the changes with gpupdate, and then restarting the computer. But the service still won't start, I get error:
Windows Could not Start the Volume Shadow Copy Service ... refer to service specific error code -2147467243
All I get in the event log is:
Volume Shadow Copy Service initialization error: the COM classes cannot be registered [0x80004015]