[The Barrow-Wight]

I think that after the War it would have become common knowledge that Denethor had been tricked by Sauron while trying to beform a valiant deed - wrest with the Dark Lord. Though he might have done it partially out of vanity (looked into the palantir in the first place), he laso did it out of dire need to protect Gondor. In the end Denethor probably held a warm but sad place in the hearts of Gondorians.