yyyy/mm/dd. Somebody added it at some point, so somebody wanted it at some point, removing it without discussion is unacceptable IMO.
Apparently that was @eht16 waaay back in 2006 (312579d); the three formats were added simultaneously on the very moment the "Insert date" feature was added. I don't think that yyyy/mm/dd (with slashes) was specifically chosen for any reason; just to provide a YMD format.
unless you have a good reason to remove existing options
Well, that's why I wanted to discuss it further... I think that having three options to provide YMD, MDY, and DMY formats is enough. I guess you cannot have everyone 100% happy like this; for example in Spain the most common format is `d/m/yyyy` with slashes; but if we're adding all the combinations of orders and separators that menu is going to become annoyingly large. So I thought it was better to keep it simple and just have the three major options; any minor variation could go through the "custom format".
Also, having each of YMD MDY DMY use a different separator kinda helps avoid ambiguity. I remember seeing some platform or program (but I can't remember _where_) that allowed you to choose between three date format options: dd.mm.yyyy, mm/dd/yyyy, and yyyy-mm-dd; just those three, each with a different separator. I thought it was a nice idea because that way one can know which format is being used based on the separators. I don't know if this is kind of a _de facto_ convention or just some arbitrary choice they made.
So in short, the reason was that I wanted to keep the menu simple and avoid drowning the user in options, and thought that having yyyy-mm-dd made yyyy/mm/dd redundant.
And that was my dissertation. If I managed to convince you then I'll go ahead with it; otherwise I'll do what you said and leave the four formats. For now I'll get rid of the translations.