they can not provide any anonymity at all, because you have to go through their system an reveal your identity. but since many bitcoin users don't care about anonymity so i guess using these debit cards is not an issue for them.
anyways i don't see any benefit for using these debit cards, first of all the fees are high so you are better off using cash or any other ways that you have been using for payment. second you are not really using bitcoin, the card provider converts your bitcoin to fiat and you use that for high fees. which IMO it means just an unnecessary additional step.