An attorney-in-fact has no legal status after the principal's death; it's not just that he cannot add or change beneficiaries, he cannot do anything.
Brenda has recapped a reasonable, but general interpretation of the issues involved that I believe would reflect the legal standard in most states. In short, a fiduciary cannot do anything that would benefit himself or herself. Naming yourself as a POD beneficiary would certainly cross that line.
However, Florida, with its millions of elderly people, has the most detailed durable POA statute I know of. It addresses the issue directly:
FSA 709.08(7)(b)Notwithstanding the provisions of this section, an attorney in fact may not:
4.Execute or revoke any will or codicil for the principal;
5.Create, amend, modify, or revoke any document or other disposition effective at the principalís death or transfer assets to an existing trust created by the principal unless expressly authorized by the power of attorney
If the POA actually says you can do it, you can. If it is silent on the issue then you simply cannot.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.