I couldn't find more info about that mandate, Not sure whether the Registrar took upon itself to issue such statements based on Government's order for the registrars to maintain accurate information of the customers(Which isn't same as the info we provide for WHOIS per domain).
Anyways, I stopped buying .in domains, Privacy is a fundamental right in India now and so I'm not sure if the mandate can be applied even if its true. Registrars here are offering privacy redaction now.
The second thing won't happen because "anonymous websites", in this context, doesn't mean anonymous from general public but anonymous from governments.
Anonymous bank accounts are also banned so do you also argue that law-abiding citizens who might be whistleblowers, victims of stalking, or have other very genuine reasons for wanting to hide their personal information will be unable to register a bank account without putting themselves in danger?
This image of controlling Internet speech by Ben Garrison always comes to mind:
1) Cyber criminals outsmarting the identification and verification mandates, because they're criminals, they're crafty, and they don't give a crap about breaking the laws.
2) Law-abiding citizens who might be whistleblowers, victims of stalking, or have other very genuine reasons for wanting to hide their personal information will be unable to register a website without putting themselves in danger.
This sort of legislation, while possibly well-intentioned, helps no one (except for stalkers, people who get a thrill out of doxxing, and corrupt organizations wanting to silence whistleblowers).