Is it really true that shifting some of the current from the copper wire to the steel armor would reduce the total heating? I.e. that the inductive heating would go down more than the resistive I2R heating? That square exponent makes me wonder, although I don't know what the formula for inductive heating would be and how it would vary with current.
Anyway, my understanding of the reason for bonding both ends is to reduce the high frequency choke effect that would otherwise raise the impedance for lightning events.
Cheers, Wayne