I have solved the problem, please feel free to point out any incongruence of errors you may find in my explanation below.
Cause:
When you create a web site root, any subsequent folder created in it, have a precise structure, with an index page of a type unknown to me and a collection folder.
By creating a folder and assigning later type_ws.webroot, and then manually creating an index.html, such html page was of a type I presume article (how can I inspect node type from share ?), but for sure of a type different from the one created automatically.
Starting a structure workflow from such index.html caused the content to not be transferred.
Solution:
I solved the problem by creating a folder xyz inside the web root, then copying the generated index.html from xyz to root, and then start a workflow from this index.html.
After approving the workflow, the content got transferred, and the wcmqs got its web site.