When you post a question on Stack Exchange, the site gets no exclusive rights to the content so you're free to publish it anywhere else that you like. In fact, since the content on this site is under a free licence, you're perfectly welcome to take someone else's puzzle and post it on any site you like, as long as you abide by the terms of the licence (credit the original author and share under the original licence).
Redundancy isn't inherently bad. If there's a natural disaster in your area and you're watching channel 2 news, you'd appreciate them mentioning the situation even if it's already been mentioned on channel 1 news.
Stack Exchange is not the best possible format for displaying puzzles. We have no interactive interface for moving chess pieces, or solving a Rubik's cube, or filling in pencil-and-paper puzzles or crosswords. Some sites are just better suited for solving certain types of puzzles. SE content is published under a free licence inherently meant for sharing, so anyone should feel free to do just that as long as they respect the terms of the licence.