Perhaps that's why Sauron's trick is to use the Palantir to show him some things while hiding others, so as to convince him that his every move would be futile.

I'm not sure even this is what destroys Denethor's mind though so much as it is the thought of the ring. He sees it as his by right of need. He sacrifices both his sons in his madness to have it, for the madness of power. His view of the world is so bleak that saving it in a way that destroys it seems "right" to him