Why isn't the US Flag at Army funerals presented on behalf of the President?

Present the flag using the veteran’s military service preferred wording:
    Army ... This flag is presented on behalf of a grateful nation and the United States Army as a token of appreciation for your loved one’s honorable and faithful service. (Note: President of the United States isn’t an official reference in the Army flag presentation.)
   Marine Corps ... On behalf of the President of the United States, the Commandant of the Marine Corps, and a grateful nation, please accept this flag as a symbol of our appreciation for your loved one’s service to Country and Corps.
    Navy ... On behalf of the President of the United States and the Chief of Naval Operations, please accept this flag as a symbol of our appreciation for your loved one’s service to this Country and a grateful Navy.
    Air Force ... On behalf of the President of the United States, the Department of the Air Force, and a grateful nation, we offer this flag for the faithful and dedicated service of [Service member’s rank and name]. (NOTE: If the next of kin has expressed a religious preference or belief, add: “God bless you and this family, and God bless the United States of America.”)
    Coast Guard ... On behalf of the President of the United States, the Commandant of the Coast Guard, and a grateful nation, please accept this flag as a symbol of our appreciation for your loved one’s service to Country and the Coast Guard.


Provided by Military Funeral Honors / U.S. Defense Department
http://www.usa-patriotism.com/reference/flag_presentation.htm
http://www.mdmildep.org/FuneralProgram/faq.html#d15