>Prepaid credit cards are essentially anonymous, as far as I know.
My understanding is that you can only buy prepaid cards after showing ID in many jurisdictions, and many other places require you to register them with ID in order to use the cards.
What jurisdictions are those? You don't need ID to purchase or register Visa, MasterCard or American Express prepaid/gift cards in the US. I've bought all of those with cash, and registered them all with nothing more than the card number and CVV code.
I have never bought them from Canada Post, but I have bought them countless other times in Canada and never showed ID for any of them.
However, in order to make certain purchases online, it's often been the case that you need to "Register" the card with the provider, and supply details that would match billing information for the selling party. I can't see any reason why you couldn't fudge that, although shipping information for real goods would leak information.
I am not aware of any places that ID for purchasing prepaid cards, let alone prepaid burner phones.
One of the way scammers get "cash" is to buy Amex gift cards with stolen credit cards. Then use those Amex gift cards to buy more amex gift cards until they feel confident the trail is murky enough. Or they use a combination of store gift cards to buy Amex/Visa gift cards.
Bitcoin thieves and malware scammers buy gift cards and prepaid cards on Rakuten with bitcoin to convert their gains to non-Internet-funny-money. Ship to the foreclosed house at the end of block. Done without anyone being the wiser.
My understanding is that you can only buy prepaid cards after showing ID in many jurisdictions, and many other places require you to register them with ID in order to use the cards.