Selecting the "Replace link" setting - often desired for the anonymous users, hides the links from admin/config/regional/i18n_translation/path, which makes the overview of the sets very uncomfortable.
I'm not sure whether the i18n module could make use of context, or is it a shortcoming from languageicons module, but I'd like to know whether I could perhaps use some alter hook to hide the language names on the rendered pages without harming the admin side.

If not, then please convert this issue into a feature request.