The main purposes of this product are to be able to mask your marketing data (name, address, phone) to businesses, and to mitigate damage in the event of a data breach (any stolen card numbers are useless).
It's not going to prevent a government entity from subpoena'ing your records and finding out what you've bought. Also, if you're buying anything that needs to be, you know, shipped or emailed to you, you're kinda going to have to give a valid address. Under the default settings, they also include the merchant information in the feed back to your bank, so your bank still gets all of the info on where you're shopping and what you're buying.
Finally, I am very skeptical of their claim about walking away from subscriptions and trials. Sure, in theory, you make it much harder for vendors to track you down, but by law, you're agreeing to pay for the company's services when you accept their agreement, and if they do bother to subpoena your information and come after you, if they find out that you presented them with a fraudulent name, phone number and address, I don't expect that would go well for you in court.