Should poets have a union and pay union dues?

[busker]

Does this mean poets will start collecting pay?  Also - how will you define a a poet in your New Utopia™?

Yeah, with an enforcement arm of sorts. 
You write a birthday poem to your woman and aren’t a union member, you get a severed hallmark card in the post next day.
I’m against such violence, but people gotta pay

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I think that would only result in creating Vogon poetry or worse.
Unfortuntately (and by that I mean fortunately), poetry is one of those things that humans will do whether you tell them they can or not.  It's like music or religion.  The more you repress it, the faster it grows. You could tell people that only the approved musicians are making the real music. You can tell them that all other music isn't music.  But people will still hum and whistle and make up little ditties or sing lullabies or around the fire or in the shower.  They will sneak out at night to play anything other than the approved music to secret crowds in ever-changing locations.
If poetry suddenly had to be officially regulated, then you can be sure the absolute best poetry will only be found in the hidden corners among the unapproved. Poetry always has and always will belong to the untamed.

I think you’re right in that if you just let people write, they will write without paying union dues
Maybe cutting off supply is the first step. Confiscate all stationery