No. Prisoners are an asset, a resource like any other. Costs a bit to maintain, but so do other kinds of military resources.
Captured prisoner is a potential propaganda tool, bargaining chip, and most importantly, source of intelligence. But if you kill them, you cannot ask them any more questions.
You also would not want your men getting too accustomed to deciding who gets executed. They aren’t butchers, they shouldn’t have to perform executions of unarmed people. No honor in it, and their lives are hard enough already. If it is decided a prisoner deserves death, let someone who executes people perform it.