Please add a checkbox (or something), so that you can turn off hyphenation of words that are connected to an em dash, and for words that already have a hyphen in them. And related to that, please always break hyphenated words/phrases/URLs at the hyphen, instead of adding another hyphen.
We currently have to search for all these "bad breaks" and this feature would be a big help.
Paul Nylander commented
Is this a difference between InDesign's older hyphenation engine ("Proximity") and the newer open-source version ("Hunspell")? Seems like switching the hyphenation dictionary in user preferences back to Proximity solves this problem (at least for US English).
Still, I agree completely. This is a fairly common typesetting rule and should be at least an option in InDesign without resorting to contorted grep styles and such.
Add option to ignore automatic hyphenation for words which contain hyphens, e.g. state-wide, non-English, etc, etc. So those words always break at hyphens.