Schema only for SYS account?

Dear community,

is it recommended to set SYS account to schema only to secure it? Documentation mentions that it's possible for admin users, but it introduces weird behavior with SYS account.

Setting to no authentication, changes are displayed in DBA_USERS:

SQL> select USERNAME, PROFILE, ACCOUNT_STATUS,AUTHENTICATION_TYPE from DBA_USERS where USERNAME='SYS';

USERNAME    PROFILE     ACCOUNT_STATUS AUTHENTICATION_TYPE

--------------- --------------- --------------- ------------------------------

SYS       DEFAULT     OPEN      PASSWORD

SQL> alter user SYS no authentication;

USERNAME    PROFILE     ACCOUNT_STATUS AUTHENTICATION_TYPE

--------------- --------------- --------------- ------------------------------

SYS       DEFAULT     OPEN      NONE

But setting it back to password authentication is not reflected appropriately. (although password login is possible)