Some contracts are highly correlated to the front month. There is no need to trade anything else. When that doesn't happen other months are more liquid. There is also needs to be a demand for hedging other months. Someone, probably more expert, already talked about commodities. But seasonal effects make different months quite uncorrelated, worth trading them if that's what you need to hedge. Fixed income. The M8 US note is similar enough to the M5 that I don't need to bother hedging my portfolio with the former if the latter will do just as well, once I've duration adjusted. But Z5 and Z8 Eurodollar are relatively uncorrelated because they are forward rates and theres a market of people that want to hedge forward rates at different points over the next few years (the metals curve is also effectively an indirect play on forward interest rates) Equity. Again very correlated to the front. Most people who need to hedge long dated equity exposure are happy to use options, or OTC. FX. Ditto. People who need to use the OTC forward market for long dated hedging.
yes, it's really a very broad question, I can answer it in a few generalities, but it would be better to ask about a single contract. Then it would become obvious why nobody has much interest in the back months and are content to do all their trading in the front month. And other contracts where storage and expected demand make the back months more active.