But - the word is used on the child - not the parents.
Look where and how the word is used. It is never directed at the parents - only as a derogative slung to insult someone, or penned on the backs for a small child.
Correction - “pinned”
The reason “bastard” became a derogatory term, rather than merely a descriptive one, is that the parents were too immoral/undisciplined to marry before reproducing, therefore were assumed (generally correctly) to have been unable/unwilling to teach morality/discipline to their child.
Used to be stamped on birth certificates too, in some places. We should eradicate the word from our vocabularies.