Maybe it is just me but I am having real difficulties trying to use the melee , even when it seems like I am stood next to the suspects I don't hit them and I end up just getting shot.

Also it seems jarring that two melee strikes will kill someone. Is there no option to incapacitate someone ?

I've also felt that the melee attack 'detection' is not quite what I expected, you have to point yourself straight towards the suspect and get quite close to melee them. Usually they take more than 2 hits to kill with melee, but you only need to hit them once. To take them out of action, all you have to do is handcuff them with the Use button. Later in the game you unlock more helpful gear like the taser, and a ballistic shield which lets you get close enough to melee someone without too much risk to yourself.