I would say that contemporary literature can't provide any insights, by definition. Because it's a slave to its zeitgeist. Anything touching politics, history, economy and especially society will be tainted.
The difference is that the books we still read are the ones that have proven to be more universally true than the rest. We only know about old books that have remained relevant in one way or another. We've long forgotten the tripe.
With modern things, we don't yet know what will remain relevant and what will fade into obscurity or lose its relevance.
Of course all literature is a product of its time but when you are reading an old book most of the time you are distanced from the events or then-new ideas presented and it's much easier to think objectively about them. As an example I'll give Marx works on communism. If I was XIX century working man I would be ecstatic about the idea, with the hindsight how communism actually works in practice I would have second thoughts. But the difference between the theory and the practice would be the actual insight. And in case of the contemporary events the actual insight would be in how they were presented and perceived when they were happening compared to how they are seen now
“Beware of first-hand ideas!” exclaimed one of the most advanced of them.
“First-hand ideas do not really exist. They are but the physical impressions produced by love and fear, and on this gross foundation who could erect a philosophy? Let your ideas be second-hand, and if possible tenth-hand, for then they will be far removed from that disturbing element — direct observation. [...] And in time there will come a generation that had got beyond facts, beyond impressions, a generation absolutely colourless, a generation seraphically free from taint of personality.”