Sometimes, additional information in images can be helpful, e.g. to indicate which piece made the last move. It's difficult to convey that information with the replayer (I guess Black's last move was something like Qa4xpc2). At other times, arrows may be helpful annotations as well.
If this is not the case, by all means suggest an edit to replace the image with a FEN string which activates the replayer. (Not both, we don't need duplicated information.) The only disadvantage I can think of is that users of the mobile apps see the PGN instead of a diagram, but the mobile apps are deprecated anyway.
I believe Stack Overflow and Mathematics Stack Exchange will not allow images and will require its askers to post their code or MathJax.
Please don't forget that there are many novice chess players out there who don't know algebraic notation, let alone FEN. It doesn't take much effort to copy code from your IDE to a Stack Overflow post; learning chess notation is a lot harder. Mathematical formulas are often MathJaxed by veteran users as well.