I have an idea for PSQ. Once the post is put on hold, the user gets the message that they need to add work/information to their post. As soon as the post is flagged, could a comment pop up informing the user that problem statement questions aren't approriate methods for requesting help? This way the OP is notified immediately not sometime later when the post is put on hold.
I do understand that one could make the argument that the flagger could post a comment, but I believe it would be much more efficient and effective if the system handled this automatically.
When some flags the post as missing context or details, I think the OP should be notified at that moment. This way they can get to editing before the post is put on hold. By waiting for the post to be on hold before notification, the user may sign off. If it is a new users, they may just abandon their post when they come back and see what happened since they have no skin in the game on the site.
As Arthur Fischer pointed out in the comments, members with 3k+ can directly vote to close. I think a prompt to the user when the vote to close is in regards to a PSQ would also be appropriate for the same reason previously outline.
Why I believe this to be the case is that many new members that have this happen to them just abandon their post when they come back and see it put on hold. If we can grab their attention before the post is put on hold, they may potential make an edit stopping others from flagging and voting to close.