macOS 11 Big Sur and later profiles require MDM

Before macOS 11 Big Sur, configuration profiles could be installed on macOS devices in several ways:
Opening a profile locally in System Preferences
Command line tools
Via MDM to devices that are MDM enrolled
FileWave could use either command-line installation or MDM, and would default to MDM when the device was MDM enrolled at the time it received the association.
Starting with macOS 11 Big Sur, Apple no longer allows administrators to add configuration profiles with command-line tools, although profiles may still be removed that way. For macOS 11 Big Sur and later, MDM is the supported path for managed profile installation.
FileWave tracks how each profile was installed: through the FileWave Client app or through MDM. Those methods use different delivery channels. To change the channel, remove the profile association and re-associate it so the profile installs through the new channel. Profile updates continue through the original channel where Apple allows that update.
Example:
Associate a Dock profile to a non-MDM enrolled device and Update Model
The profile installs using the FileWave Client app
Enroll the device into MDM later
Update the dock profile and Update Model
The profile update continues to use the FileWave Client app delivery channel
Newly associated profiles would though be handled by MDM.
Remove the association of the Dock profile, Update Model
Once removed, re-associate the Dock profile and Update Model
Because the device is now MDM enrolled, the profile and future updates are delivered through MDM
Note that not every type of change that a profile makes can be cleanly undone simply by removing the profile. One example would be if you add a printer via profile and then remove the profile the printer will remain. Always test adding and take a look at what happens when removing a setting. 
Impact
This matters when devices are upgraded to macOS 11 Big Sur or later.
Be careful with profiles that provide network access, certificates, VPN settings, or other connectivity requirements. If you remove a profile that keeps the device online, the replacement profile may not install until the device has network access again. FileWave does not automatically switch the delivery channel for existing profiles for this reason.
Devices not MDM enrolled
Where devices are not MDM enrolled:
Any associated profile would have been installed using the FileWave Client app before Big Sur
After upgrading to Big Sur, profiles would remain installed
After the device is on Big Sur or later, profile updates fail if they still depend on client-side profile installation
Once on Big Sur any new profile associations will also fail
Disassociation of a profile will remove the profile
Device MDM enrolled after profile installation
The same client-installed profile concern applies before MDM enrollment. After the device is MDM enrolled:
Any new profile association installs through MDM
Removing the association, allowing the device to remove the profile, and then re-associating the profile installs it through MDM
This is the same impact even if not upgraded to Big Sur
Resolution
Managing profiles on macOS 11 Big Sur and later requires MDM enrollment. Without MDM, profiles may fail to install or update.
Where profiles were installed not using MDM, the only way for these profiles to become managed is by removing the association, allowing the device to remove the profile and then creating a new association.
Plan profile removal carefully when a profile controls network access, certificates, or VPN. Those transitions may need a manual or staged path so devices do not lose the network they need to receive the replacement profile.
Additional Information
If Client Info does not show a Command History tab, the device is likely not MDM enrolled. In that state, only the FileWave Client app can install Filesets. Apple's VPP workflows also require MDM.