As someone who used to make hairballs for Liquid-Plumr commercials for a living, I can attest that it is possible to clog drains with short hair. The demos were made with soap and short barbershop hair trimmings. You may need to take a wad of your hair, coat it thoroughly with soap, remove the trap and then compact it like you are loading a curved musket, but it’s possible. You will then be able to marvel at how a little bottle of overpriced toxins can clear it up in a jiffy. Give it a shot some Friday night when everybody else is out on the town and you are home watching Streets of San Francisco
PS: I’ve used a 3/8" spacer on hair clippers for several decades. 
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