There is no connection between archival quality and the use of blix or bleach-fix. The argument is removal of silver from color films which affects grain, sharpness and color repronduction. In E6 films, it can also affect whites.
So, your question misses the true problem.
A post development treatment of color film (any type) must remove all silver metal and all silver halides. The fix part of a blix or a bleach-fix does remove all silver halides present, but the bleach part may not allow removal of the silver metal completely and that is the problem. It does not affect image stability though.