Potential flaws:
(1) They used to have a bit of overhead (1-5%). Not sure nowadays.
(2) None of that is ironclad anonymity. Don't be an outspoken gay ukrainian hacktivist journalist visiting russia or anything.
(3) Some organizations will only do business with you if they're able to slurp up more data than the initial transaction would suggest to a reasonable person. You can't use prepaid phones to sign up to many online accounts (notably Facebook for a long time) because the site owner can't slurp up your address and other info without certain postpaid plans, and you can't use any pseudo-anonymous card [0] to make transactions at a place that wants to buy your address and purchasing habits from the card issuer.
[0] Solutions like privacy.com might qualify here perhaps, in that you can actually anonymize your name/address/... and still use most of the sites trying to capitalize on that data, but fundamentally that just turns them into a middleman with the same data, and I expect they'll sell out eventually. Plus they have raw access to your bank account and other things you might not want to give out.