Literary Magazine Thought

Has a literary magazine (I’m using literary as those who publish fiction/poetry on a regular basis) ever had a model where a reader can pay a writer? 

I am curious because I think it would make an interesting dynamic to the publishing game.  After the base amount paid by the magazine, readers would be free to pay a writer if they think his/her piece has merit or if they enjoyed it.  Readers could send the checks to the magazine, who would then pass them on to the writers.  Sure, it would take some really honest staff at the magazine and some really cool readers but this could be good if done right.

Or maybe it would be dumb because of theft, crossed wires, overwhelmed staff, and all kinds of other things but if someone COULD figure it out… awesome.  The payment could even include a note from the reader about what reached them or made them think.

Just a thought…