It does not say that in the Illinois statute. It says it in the Florida version, but not the Illinois version. Each state legislature makes its own decisions about how specific a statute should be.
However, the fact that the Illinois statute does not list the things an attorney-in-fact cannot do isn't really relevant. What the statute does say is:
(755 ILCS 45/2‑9) (from Ch. 110 1/2, par. 802‑9)
Sec. 2‑9. Preservation of estate plan and trusts. In exercising powers granted under the agency, including powers of amendment or revocation and powers to expend or withdraw property passing by trust, contract or beneficiary designation at the principal's death (such as, without limitation, specifically bequeathed property, joint accounts, life insurance, trusts and retirement plans), the agent shall take the principal's estate plan into account insofar as it is known to the agent and shall attempt to preserve the plan...
Albeit general, that's a pretty clear instruction to the attorney-in-fact not to go around changing ownership and survivorship provisions willy nilly. That's true no matter whom he would suggest as a preferable POD beneficiary or joint owner. When he wants to name himself as the beneficiary his actions and his judgment are doubly suspect.
Clearly, the specific language of the POA could override that general instruction. If it doesn't then the general instruction controls. Again, your bank's attorney needs to say grace over this; this decision should not be controlled by someone whose legal arguments are always based on: "Show me where it says I can't do that..."
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.