Since I've been known to rely solely on knife and throwing knife kills during whole matches, I reject your proposed changes to the melee system.
If a person is able to take a full running sprint towards you and kill you while you're firing at them, you need to aim better (unless you have a sniper rifle, then you're usually just boned). The only thing that makes knifing really effective is that you catch people off-guard and they're not used to shooting a moving target in such close proximity. They panic, and their accuracy goes down. Take the time to aim and you won't suffer any more of these deaths. Spray and pray only works if you're the one with the drop on them.
As far as your legal, realism argument, you mentioned that civilians survive a knife attack lots of times, so imagine trying to kill a trained soldier. To that I say that the opposite is also true. Just because someone was attacked with a knife does not mean said knife-wielder attempted to kill them. Their motivation could have been as varied as mutilation to a "to show you I'm serious about taking your wallet, I'm going to cut you". Yes, murder may have been the intent as well. Second, the knife-wielder in question (game-wise) is a trained soldier who is taught to use every weapon (including a field knife) to it's supreme efficiency. If you know where to hit, your knife is sharp/big enough (not necessarily Dundee-sized, but it can't be really short either), and you're strong enough to pierce through breastplates and soft spots in the skull(easier with sharper/better knifes) it's completely feasible to finish someone in one shot. There's a lot of x-factors to this, but I don't think it's into the realm of unrealistic.
Plus, it's a game. If I wanted realistic shooters, I'd join the armed forces.