Can an individual with power of attorney apply for and receive a card in the principals name?

It depends upon the reasons the POA is in force. If the POA is due to a person not being able to handle their financial affairs such a transaction cannot legallt be done without permission from the court. In cases where credit is obtained using power of attorney w/o court approval, the POA holder is made a joint account holder and will be equally responsible for any debt. There is often confusion about how much legal authority someone with a POA is entitled to pertaining to the financial and personal affairs of the issuer. Any action taken by a person holding POA is subject to investigation by those agencies empowered to do so. If POA abuse is found valid the person can face numerous criminal and civil penalties as defined by the state laws.