I think that that would be a bad idea. Archived caches are usually archived for a reason. As some of the others have mentioned, sometimes it is very much not supposed to be found after it has been archived.
Groundspeak has one more level of sanctions to prevent people from logging caches that are long gone: They can be locked as well. When a cache is locked, no further logs can be added to it. It is not typically mentioned on the cache page itself and is only made visible to those who try to add logs to it.
The locked state does not care whether you
- Found the cache well before it was even archived (if for instance you are behind on your field notes) or if
- Have just recently discovered that there is a cache that you simply have to have and thus went ahead and logged.
Locked means locked - for everyone. Any list such as the one suggested here would increase the amount of logs that archived caches get. That would very probably lead to an increase in locked caches, which would not only hit the second category above, but also the first.
For further reference on the concept of locked caches there is some context here - a forum thread in which I complain about not being allowed to log a webcam cache that I had ample documentation for having found back in 2013 - to no avail, I might add.
There is another reason to not list archived caches: Sometimes there are regrets. The cache owner may regret having published it and the rewiever might do the same. That may happen if for some reason adequate landowner permission has not been obtained or if permission is revoked - or that the searching cachers destroy some delicate nature or historical landmark. In those cases there is a wish to get the cache off the grid as soon as possible. Unfortunately, once a listing has been made public, it can only be archived (and locked) - its publication cannot be revoked.
In that case, there is no interest on the part of whoever wanted it archived to have it listed anywhere. It should remain that way.