Sad that you ask a question in English based on a discussion in French... and this help site is not the right place to talk about disputed stuff (better on the forum or one mailing list).
Anyway, I will repeat my argument here : the relation "associatedStreet" is supposed to represent the street and its house numbers. The tag "name" should not be used for another purpose like routing instructions etc but just give the street name itself (as an optional hint, as said [on the wiki][1]). Otherwise you create unnecessary confusion if the tag name differs between the relation and the highway, especially for newcomers.
In addition, I could say that OSM is a geodatabase as you know. It's not necessary to write in plain text which segment is 'north' and which one is 'south'. It's all defined in nodes coordinates. We might have to create some additional tags helping navigation systems but certainly not in the street 'name' tag itself.
The point you raise about the editor, that it should display the 'name' tag from the street member is hard to solve and support in long term. Basically, the editors display all relations in the same way. They cannot check each relation members based on all possible relations types to find which one contains the expected 'name' text.
text to display on the info widget.
[1]: http://wiki.openstreetmap.org/wiki/Relation:associatedStreet
