If "we have to do it this way because this is how it's done" was how you all were planning on living your lives, you wouldn't be doing poly at all. :P
Seriously, just do some internet searching, you'll find lots of counter-examples of poly done without labels and hierarchy.
The major players. Me, 30ish bi female. Gia, girlfriend of 4+ years. Clay, boyfriend/dom. Davis, ex/friend/"it's complicated." Eddie, roommate & fwb.
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy and Nikki, Clay's partners. Liam, Eddie's husband.