Part of that answer could be due to Théoden's (Bernard Hill) enchantment by Saruman (Christopher Lee), compelling him to protect Wormtongue, who had Saruman's backing. Many would likely not want ...

To watch a Bernard Hill performance was seldom to see capital ... to him in the grip of possession by Saruman, via the vicious Wormtongue, and when the spell is dispelled, Théoden is allowed ...