It's not really about playing with friends per se. It's about forming a team beforehand that lasts for more than one game. The NFL would be unrecognizable (though probably pretty amusing) if random dudes who didn't know each other and had never played together get thrown together for a team every game and had to figure out how to coordinate and communicate.

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Rioters participate in an internal tournament with permanent teams. It's a pretty amazing experience for the people that join in. You practice with your team. They can help point out mistakes and even learn to correct for your weaknesses. You learn to read each other's tells and almost read each other's minds. Pros have that. Very few normal League players ever get to experience it. Dynamic Queue was trying to offer that experience to more players. It's just a different (and frequently better) game when you just know how that ADC is going to jump in or how your Jungler will gank without relearning it every time.