This [unfortunate] situation is a consequence of the rules of the language (F90+) for intrinsic assignment of derived types. The details are spelled out in F2008 7.2.1p13. As a summary, intrinsic assignment of derived types (the assignment that happens with the wrapper_assign specific commented out) does not invoke non-type bound defined assignment for any components that are of derived type. In F90/F95, if you want defined assignment at some lower level of the component hierarchy then you need to have defined assignment for all the parent components up to the base object.
F2003 added type bound defined assignment to the language and this is invoked by intrinsic assignment of derived types. Use that instead of the stand-alone generic form of specifying defined assignment. (This also avoids a potential problem with the type name being accessible but the defined assignment procedure not being accessible.)