Depends on the "hero".

Hard as a coffin nail, ex-Three Letter Acronym commando ninja? Agree, they shouldn't be leaving a weapon they can use. And if they can't carry it, they'd put it out of useful condition.

Flustered suburban parent thrust into a situation out of their control? Disagree, they're more likely to harm themselves with a terrorist's assault rifle.

At least the opposite occurs in movies like Black Hawk Down where the operators were shown taking the magazines from dropped weapons - they knew the next man along would just pick it up and point it at them.