They need to be aware of what they are promoting with thier tv show. If it is a comedic show that is one thing, especially if it is satire or absurd, but they still need to be serious about their work and work hard at making it the best it can be.
Yes, because many young people look up to them. Famous people have to think many times before saying or doing anything in public. They have to be examples of good public conduct and share these examples with the new generations. Not the books nor parents are important in mental education nowadays, but the public personalities.
Yes, entertainment personalities need to take their shows seriously. The success of the show depends on how much effort and work these personalities put into them. Whether it's a talk show, a comedy show, a game show, or anything else, the television or film personality must work with the show executives to make it a success.
Sometimes an ironic sense that the host of a television show isn't taking their show, and themselves, too seriously can enhance the entertainment value of the show. It can create an irreverent tone and feels more accessible for the viewer. When presenters insist on taking lighthearted shows too seriously, the result can often be fairly ridiculous.