Can I publish a paper which 1) proposes an idea and 2) proves that the idea doesn't work?
What is wrong with proving some never existing idea is not a good idea?


Ideas are easy to produce, but unfortunately only a tiny fraction of them are really useful. If you pick an idea at random, it's likely to be not a good idea, and in most cases it would be relatively easy to check it and see it. So, your referees and your editor may wonder why is it so important to publish this random negative result, particularly in competition with other ideas, which actually lead to improvements and positive results. 


  why-science-needs-to-publish-negative-results


Some negative results are indeed worth publishing. For example, when you consider not a random idea, but a mainstream direction, which is believed to be superior all the time, and demonstrate that for a particular class of problems, or in particular setting, it does not work. So, your negative result essentially is an important warning that some popular and blindly trusted method is not yet well understood and should not be used as a silver bullet. Publishing such result can help preventing serious mistakes and hopefully start important discussion, eventually leading to improvement (or ban) of existing methodology. 

Even in this case, you will need to do a good job convincing your referees and editor that this negative result is worth publishing, particularly if they are stand behind the idea you prove to be not good. Academia is very much influenced by the modern culture of success. It's much easier to become successful in academia when you talk about your success (however marginal and simple), rather when you produce negative results (however important and difficult).