I understand the technical reasons.
But is there a way to have an email reader click on a link that would allow him to join a group in one click (if he is connected), or just after connection (if he was not connected) ?
Yes, if they're logged in you can use the below URL structure for example to join a group.
index.php?option=com_comprofiler&task=pluginclass&plugin=cbgroupjive&action=groups&func=join&cat=CATEGORY_ID_HERE&grp=GROUP_ID_HERE
You should also be able to generate internal Join links from backend on the Menus page if you'd like it to be a Joomla menu item, etc..
In general, how is it possible to avoid to return to the home page after connection but continue to the page requested ?
Well, you could set a login redirect URL within your CB Login module and it'll always send them to that URL.
Another solution would be to have GroupJive as a module inside an article : is this possible ?
That way, the article with Registered rigths would first ask for connection, then show the GJ.
Don't think that'll matter, but suppose you could try.