I don't care that Denethor thinks the palantir has revealed to him the death of the West. I don't care that Denethor is grief stricken about both Boromir and Faramir.
There is a war going on... and Denthor's duty is be on the walls fighting. Not dissolved in self-pity. Not descending into madness and grief. He is the Steward of Gondor, and the people are looking to him for direction and strength. Stand-up and do your duty.
I think Denethor's failure to do his duty is so contrasted against Frodo's valiant courage. Frodo is afraid too. Frodo thinks his life is over. But, still Frodo goes on. It will take Sauron himself to stop him. Valiant little Frodo. And Sam!
Boromir, that's why your daddy isn't king.