It looks like it only cares if you enabled it, but if you blank out the password, it will drop the username.
With password set:
{'localStatusPageEnabled': True, 'remoteStatusPageEnabled': False, 'securePort': {'enabled': False}, 'localStatusPage': {'authentication': {'enabled': True, 'username': 'admin'}}, 'namedVlans': {'enabled': False}, 'fips': {'enabled': False}}
Password blanked out:
{'localStatusPageEnabled': True, 'remoteStatusPageEnabled': False, 'securePort': {'enabled': False}, 'localStatusPage': {'authentication': {'enabled': True}}, 'namedVlans': {'enabled': False}, 'fips': {'enabled': False}}
Password set again:
{'localStatusPageEnabled': True, 'remoteStatusPageEnabled': False, 'securePort': {'enabled': False}, 'localStatusPage': {'authentication': {'enabled': True, 'username': 'admin'}}, 'namedVlans': {'enabled': False}, 'fips': {'enabled': False}}