So exactly what crime did he commit?
If a man says he can’t breathe he is necessarily in distress. If you have your arm locked around his neck you should reasonably assume that you are contributing to that distress. If your motivation is to keep him from killing a child standing nearby, then by all means squeeze away. If your motivation is to avoid showing weakness you must relieve his distress and reassess your tactics.
Let’s turn it around, shall we? Does a cop ever have to use discretion when making an arrest? Let”s say that a pregnant woman “resists” by simply saying, “But officer...” Does he have the authority to slam her down? When he does this might she not react like a normal human being and begin to struggle to protect herself and her child? If she does? ? Out comes the nightstick.