Scotman, you are right, of course. Eggheads isn't JUST a quiz show in the way that University Challenge and Mastermind are, and Fifteen-to-One was. It's part quiz, part entertainment, and a certain amount of showmanship is expected. You are right that, unlike the above-mentioned shows, it wouldn't make good telly for the Eggheads just to answer straightaway every time, though they do that sometimes. It's also important that the public thinks that the opponents have at least some chance of winning, even if the opponents generally don't, and are mostly there just to get on the box.
I can assure everyone that the Eggheads really do not like to lose, and the chasers even less...