You don't get these problems with economics. In economics journals its standard practice to include your specification, as well as the whole regression output, including a full list of included terms and their significance tests.

When I was completing my Master's degree I was a sessional assistant for an introductory quantitative methods course for economics and finance majors. The type of simple linear regression would be considered overly simplistic at that level (at least in the absence of some simple specification testing), and if the j curve is already accepted in medicine, to model linearly is unforgivable. It's not like non-linear transformations are hard to do either, you can do them in Excel without too much trouble.

FWIW, I'm of the impression that economists get a better grounding in quantitative methods than other social scientists (and I would say that the profession is a bit too keen on mathematical approaches in some cases), so maybe you would have similar problems with psychology or sociology. But I don't think economics has this problem.