We all call them "birdies". Shuttlecocks sounds too posh.
I watched a video of how shuttlecox are made and they certainly seem to have way more quality control than any pickleball might. Not cheap either, mine (AS 50s) are $4/bird and more times than not, we're lucky to get two games before they break a feather. When these are finished, I think I will go back to Ling Mei 70s.
BTW if you ever visit the stringing forum, I have a thread titled The Grand Experiment you may or may not find interesting.