When those rules were written in the 1970’s they were to assure players that the lottery was on the up-and-up and that some real person DID eventually win the prize.
But today, with the internet, GPS, reams of data about everyone online, hardened criminals surfing the web, violent gangs, etc.....there is a real good argument to be made for changing this.
What you describe is why the question is moot. Lottery winners become known, formally or informally.
True anonymity allows politicians and their cronies to hijack even more money that isn’t theirs.