Sure they don't! Haha.
Exhibit A: Riley's undercoat.
I just wrestled this hair out of Riley's undercoat in the bath using conditioner + a deshedding rake in preparation for her full body clip later today. Keep in mind this is WET undercoat and is easily 5x this volume when dry. Empty toilet roll for scale, I tried to make the hair about the height of the toilet roll. :p I got another pile like this about a month ago and will get another in April. Ahh, Spring coat changes! Thank goodness Toby appears to be single coated lol.
There are plenty of doodles who don't shed BUT then again you can get a hairy monster like Riley who is a ridiculous fluff factory :)