I've been on both sides of this insisting, if a company annoyed me too much (e.g. headhunters mailing too frequently) I'd drop the "data privacy laws" (nowadays GDPR) bomb and ask for my data to be deleted.

On the other side, a customer got really pissed off by an online shop we maintained for a client, and asked for his data to be annihilated, we thought "What a douche.".