Not every puzzle is a good fit here.
In particular, the Stack Exchange network uses a question and answer format and is generally looking for questions that actually have AN answer, making “list requests” (questions like “What word puzzle sites are there?”) generally not accepted because they cannot be answered definitively. While Puzzling.SE turns things somewhat head over heels in that in many (most?) cases the person posing a “question” already knows the answer and is challenging others to find it, we still follow most of the norms for the Stack Exchange network.
Here’s the guidance I usually offer:
Puzzles with no "right" answer are generally discouraged; you should have some objective criteria, even if arbitrary, for determining the "best" or most "right" answer, so that we're not just assembling a collection of alternate answers.
So while we do have puzzles here that are open-ended in that the best answer is not (necessarily) known at the time the question is asked, criteria are given as to what answer will be deemed the best. This is pretty common for word game puzzles that, for example, might challenge answerers to find the longest dictionary word that is a simple concatenation of three letter dictionary words, or the highest scoring word that can be played as a first turn in Scrabble using a particular set of tiles, or the like. Even if not particularly interesting or good, these examples would be on-topic puzzles that could be asked here.
But an open ended challenge with no objective criteria for determining a “best” answer among many valid responses would be closed as “Too Broad” because, well, that’s essentially the very definition of what a Too Broad question is - one with many possible answers, none of which is clearly the “right” answer. Such questions might be valid and interesting puzzles in their own right, but they do not fit how this site works and so would not be appropriate here.
One final thought - there is a difference between Too Broad, which is what your concern about many possible answers would run afoul of, and Off Topic, which is itself a (different) reason for a question to be closed. A question that has a single answer, or an objectively measurable “best” answer, may be safe from being closed as too broad but still be off topic for the site it is posted on (or perhaps for ANY site here). For example, we frequently see math questions asked here. Some are just questions that you have to figure out how to solve, which might be puzzling for some but by no means a puzzle. Others have a definite puzzle vibe - there is a key element of the unexpected, what we’ve called the “aha moment” - that makes them puzzles and not mere math exercises. The former are actually off topic here because, while they are something with a right answer that the asked wants us to solve, they’re not puzzles. Word questions, similarly, may not always be actual puzzles.
I hope that helps!