How do I objectively choose a statistical approach when I want to publish?

It is a common concern to hold alpha values at 0.05 and that it is completely arbitrary. I have been interested in using other methods, but I know that there may be pushback from editors to use standard statistics rather than weighing type I and type II errors and choosing an alpha value from there. I've seen it done before, but how much is the real drawback from doing that in publishing?