If there are shitos that mean the plastic big is unnecessary, it would appear that doing so is not really a Halacha but a Midas Chasidus, and would therefore be discouraged.
WADR, this is completely untrue. Just because there is a valid Machlokes doesn’t make the “Machmir” side Middas Chassidus. It means that even B’dieved, one side holds it is Assur.
The prototypical example of this is the Machlokes Bais Hillel & Bais Shammai regarding Tzaras Ervah. Bais Hillel actually held the children of such a union were real Mamzairim, not “Middas Chassidus” Mamzairim.