Q makes a lot more sense if you consider the whole thing to be a charade. He doesn't have any intention of killing Picard or any of his crew, or even stopping them on their mission. He does want to put on a show for the rest of the Q continuum to demonstrate the humanity won't revert to their worst impulses under stress.

Likely, what he ultimately wants is a solution against the Borg. They're a tricky one for the Q to deal with in more direct ways. Something like how Gandolf can't directly attack Sauron at full power, because when gods fight, the world tend to break apart.