With larger shields, such as a Roman scutum, that wouldn't be too much of a problem. In a tightly ordered formation it'd be risky, since it would expose oneself and the person a shield should protect, but in a less orderly melee it'd be quite viable; particularly if the eye of the enemy is on the sword arm.
Edit: sorry, didn't properly read the last few lines. It's correct that the shield would usually be used to unbalance an opponent with a knock on the jaw, actually killing someone would be comparatively rare.
It'd be interesting if some (reenactment?) experts could shed some light on what is possible, viable in battle and actually useful.
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