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While it is definitely true that minimal examples are sometimes asked for reflexively, and it's possible to make questions that shouldn't require them, (see automatic check for MWE) for some prior discussion) I don't think that discouraging MWEs is at all the way to address the problem you are raising. Here are some counterpoints to think about (some are the same points raised by Ulrike Fischer in her comments):

1. Questioners generally want to solve specific problems. But much of the time it's hard to tell what they are trying do without a MWE. And removing the need for a MWE doesn't make the specific problem go away and the question more general. Also, things like document class can matter a lot, even for general questions: how to change section titles is a general question, but doing it in the standard classes vs. memoir vs KOMA requires distinct solutions. Similar points can be made for font questions and bibliography questions, among others.

2. Even general questions can benefit from a MWE. What makes them general is not the lack MWE, but the specific question asked along with the MWE.

3. Questions without examples can easily lead to XY problems. MWEs go a long way to clarify issues so that bad solutions don't get encouraged.

4. Answerers are volunteers who give up their time and expertise to answer questions. Providing MWEs as starting code saves time and encourages answers.

5. The "generalization" problem works in both directions. Depending on your level of expertise, applying a general solution to your specific problem may or may not be difficult. This relates back to point 1. Conversely, applying the method used in a specific problem to a more general one may or may not be difficult.

6. The site doesn't operate on rules, generally, but on conventions that people follow. So talk of "abolishing" anything is really not terribly productive.

Some other alternatives

I agree with the main point that answers to very specific questions may be of limited use to others, but there are ways in which answers can be made more general.

1. If you answer a specific problem, think about whether there is a more general version of the code that would be useful to others and include that in your answer.

2. If you think that there is a general question that would help others, ask it yourself, but as with point 2 it's still helpful to have an example to work with.

3. Do what you think is best to help the site, in your own behaviour but don't try to legislate behaviour of others.