I think Hellman mentions that the prototype chip was designed to be installed onto a recently deceased body, which would then take over and physically modify the brain (via nanites) to the persona on the chip.
V is an extreme case of the chip being installed on a still living body (specifically it is installed while V is still alive, and then when they die, the chip boots up to begin its processing).
Unfortunately, since the chip is designed to "takeover", it causes irreversible damage to V's physiology, so that even when V is turned into a chip, the body has been modified to match Johnny.
At least, that's how I understood it.
My only guess on why V's chip cannot re-modify the body is because the changes made by the chip were designed to work only once. The dialogue in the game seems to suggest that it can no longer be reversed.
It's also not clear whether the engram that V is turned into is the same as the prototype that Johnny is in. V's engram might have only been made to store their information, whereas Johnny's experimental engram was designed to take over a body.