First, before I forget I wanted to mention that I am in full agreement with you on the importance of translating an-atman as "no abiding self. In fact, the Chinese first translated this term with three characters, i.e., no - eternal - self. Later it was 'shortened' to just 'no-self' and, as you will see in my new attached article, this has contributed to yet more death and destruction!
None of this will amount to a hill of beans for those unconcerned with Buddhism. But for those who are concerned with Buddhism -- either by practice or as part of an intellectual toy box -- I think it is pretty goddamned important.
Using shorthand expressions is common enough. The underlying premise is that everyone knows the warp and weft of what is being referred to. The difficulty lies in the fact that sometimes others don't know the warp and weft and are reduced to taking the short-hand version as the long-hand fact.
I haven't got the energy here to do all the brightly-lit arguments about how short-handing no abiding self leads to nihilism or how no abiding self is a much more delicate and intricate proposition/fact ... the kind of assertion that means some hard work will have to replace a simplistic absolutism: If it ain't something and it ain't nuthin', then what is it?
For Buddhists, I think, the matter needs to be front-and-center as they issue their wise nostrums.