"some companies.. including the federal gov't, already have in a
"mileage
allowance" "

Actually, this is something set by the IRS. If a company pays you more
than the mileage allowance (this is for cars) you must show receipts to
the IRS that your vehicle costs more to operate, otherwise you will be
taxes on the difference as ordinary income.
The IRS would actually be quite irritated if you took a car milage
against an aircraft unless you also provided documentation that you
spent at least that on the aircraft. You can not just say "give me the
mileage allowance and don't ask how I got there".

Remember, the mileage allowance is a nice goody the IRS gives us by
saying reimb. at that rate does not require supporting documentation.