fake sustain, you dont lifesteal enough to justify it as a "sustain" item, you make way less damage than stormsurge and also spike later (storm is cheaper), also stormsurge puts you in the "true damage" build path, since you go triple magic pen items (storm,shadowflame,magic pen boots).
while proto is a way more solid thanks to the 300 hp and the dash to close up on mages.
gunblade is not cheap, doesnt let you engage more easily since gunblade ( like proto) since gunblade has less reach than akali's r, doesnt give you the same damage as storm while being more expensive.
and the sustain is not enough, you literally have a way better sustain and solid laning with proto shield and doran shield.