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.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.