Even if you have a Trust, you still need a Power of Attorney because it applies, during your lifetime, to management and control of your property that is not in a Trust.
Certain property does not get put into your Trust during your lifetime and some of your rights do not belong to your Trust. Examples include social security rights, personal income tax returns, and qualified retirement plans.
Your Trustee has no authority to prepare and sign your personal tax returns or speak to the I.R.S. about your taxes. The Trustee has no power to redirect the deposit of your social security benefits or make social security and Medicare benefits elections. Your qualified retirement plan accounts cannot be titled to your Trust during your lifetime or the I.R.S. will treat that as an early withdrawal, assess taxes and penalties, and refuse to honor additional deposits or earnings as tax delayed. If they are not titled to the Trustee, then the Trustee will have no authority to direct investments, elect withdrawals, take out loans, etc. The Trustee also has no power to transfer into your Trust any property you accidentally forgot to put into it.
The agent, or “attorney in fact,” named in your power of attorney can handle those non-Trust matters if you become incapacitated. It is customary (though not required) to name the same person as Trustee and as attorney in fact, so that control of both Trust and non-Trust matters are centralized with one person.