I learned the hard way that The New York Times doesn't usually run quip puzzles, when the editors told me in a rejection letter. Are any of the other usual publishers known to accept and run quip puzzles? What's the general sentiment among creators regarding quip puzzles?
To add what's already been said, quip puzzles can usually be pretty bad on the "solving experience" end, too. The problem, a lot of the time, is the quip needs to be novel, entertaining, and fairly known at the same time for the idea to work well and come off as fun. Minus the fairly known aspect, for average-skilled solvers, quip puzzles usually turn into downs-only solves around the entries and make solving the puzzle a lot more of a chore as a result for guessing the quip words. So the payoff needs to be higher at least in terms of the entertainment value. Inevitably, some kind of quip quote that just happens to give the constructor a giggle, (or even worse) something the constructor made up themselves, falls short on that. Just better off to not.
(Same argument for "group" type themes, wherein it holds theme entries of random words that have something in common.)