For many questions (although not all), a MWE is helpful (see, e.g., Should minimal examples be required, or just encouraged, for questions to be answered?). However, many posts don't include one (especially in case of first time users).
It has been proposed to add MWEs to other people's posts by editing (Should minimal examples be completed for the submitter if they only provide a code excerpt?), but this has disadvantages, the OP not being forced to provide research effort being one of them.
Currently, the Ask Question page does not mention MWEs directly, and also the linked How to Ask etc. are not clear about this (if I'm not overlooking something). Adding to this may help increase the number of questions with MWE.
However, a more direct approach may give better results. If the OP tries to post a question without the text \begin{document}
in it, a warning can be issued. This warning should be polite to cover cases where a MWE is not necessary. Would this be a good idea or are there disadvantages I didn't think of?