Why must the game revolve on which team has the better adc?

It feels as if, if you don't have a good adc then you are bound to have a hard time carrying because no one will have the guts in your team to engage. I feel that ADC's need to be useful in other ways besides doing all the damage, not to mention this is coming from a guy who used to be an adc main. Now that I tried playing other roles besides adc I now know why so many people complain about adc's.