There are some elements of the Chase that are a bit irritating, to be sure -- the debate over which amount of money to take is just a waste of time, really. I would have made my decision which amount to go for before even seeing the options (the middle one, always). But at least they ask a decent amount of questions and the speed rounds are great fun, I find, as I enjoy paced buzzer quizzing.
The age thing, though. I think it depends rather on the topic. If it is a popular culture question then it will depend again on how famous the band or show was, but many cultural aspects of the 70s or 80s stayed there and in those cases "it was before my time" is actually a fairly reasonable excuse. There's plenty of stuff to listen to in modern times to keep track of and it might depend on the channels you watch, radio stations you tune into, etc etc., as to whether you have a chance of recognising the B side of a less-famous song by some group only briefly popular in 1967 if you weren't alive at the time.
Politics is a bit different, but then again there is a case for it. It's about what is or feels relevant to you. For some, the politics of the 50s and 60s is likely to be as relevant to them as 19th century Prime Ministers are to older people (ie, not very -- go on, who came after Peel's second term?).
Age is half an excuse, although there are some seriously good young quizzers around if you'd care to go looking. The problem is that they aren't always so likely to appear on cash-related quiz shows.