I learned to play mafia somewhere else. And it was like a middle ground between the no claiming and mandatory claiming. Closer to no claiming.
You were never made to claim if you were being wagoned. It was not a requirement to be lynched or not.
So most games I never claimed. HOWEVER if you were being wagoned and a lynch seemed likely and you were the town cop or doctor, you’d then claim to not get lynched. Now at this point scum could counter claim you since no one else has probably claimed.
So it then became a fun game of which person claiming doctor is lying. That was fun unless you were the real one with the role and losing to scum.