If the conductor is protected at or below it's ampacity it is no different than a feeder or branch circuit conductor. 240.4(F) says it is protected if the conditions mentioned are applied.
Whether or not the conductor is protected at or below it's ampacity is irrelevant to supplying another conductor from it.
240.21 says that conductors must have overcurrent protection
AT THE POINT where the conductors receive their supply
EXCEPT as specified in 240.21(A) through (H). The transformer secondary conductors
DO NOT have overcurrent protection at the point they receive their supply. The have overcurrent protection on the transformer primary
AS SPECIFIED in 240.21(C).
240.21 also says that conductors supplied under the provision of 240.21(A) through (H)
SHALL NOT supply another conductor except through an overcurrent protective device meeting the requirements of 240.4.
In the image, the #4/0 conductors
CANNOT directly supply the #6 conductors (even if the #4/0 were properly protected). To do so would be a
VIOLATION of 240.21.
I don't know how else to say the same thing. You can't use 240.4(F) as an excuse to violate 240.21.
240.4(F) is saying under certain situations this protection is on the supply side which makes it no different than a feeder or a branch circuit conductor - whichever applies depends on what is supplied.
240.4(F) doesn't say any such thing. Transformer secondary conductors are already feeder conductors (or possibly branch circuit conductors) by definition. Also, 240.21 makes no reference to 240.4(F).