Reading around the boards I feel like we don't hate the DQ system.....
We just hate the premades.
We love getting the role we want which this system provides (apart from the 2ndary sup mains who get sup 90% time instead) but the truth is we hate playing with and against other premades especially in ranked. We are meant to get ourselves out of bronze with our own skills not piggy back your diamond friends or lack of them.
Either bring back old solo q's restrictions (max 3 leagues between the pair and max premade of 2 people) or seperate the premades from the solo qers (with this system you arent allowed to have premade of 4 as this forces a solo qer joining that team).
Personally I love the system since i don't have to fear about getting adc or sup any more but I do hate having people who are obviously way higher skilled than me facing me cuz they have someone the same level as me on their premades