No, let's not do that, first of all because the premises that every post has an associated chatroom is flawed.
There are two possible options that lead to the creation of a chatroom that gets "linked" to a post:
- Only two users go back and forth 5 times in comments under a post and they get offered the "let's continue in chat" link which one of the participants then clicks.
- A moderator uses their "move comments to chat" feature.
Both actions leave a comment under the post with a link to the chatroom which is visible enough I think.
Comments (and chatrooms created for posts) should really only be used to clarify a post so it can be edited into shape. If extended, long lasting discussion is needed an relevant for posterity there is most likely something else wrong with the post. Fix that instead of having a third place where knowledge collected. Keep in mind that chatrooms that don't see traffic will be frozen / deleted after 6 to 8 days which will render them useless for anyone with < 10K of reputation.
I checked on chat.stackexchange.com and there are currently about 360 chatrooms that are imported from discussions under posts and 3291 pages of them if I take frozen/deleted rooms into account. I think that also shows there is no lasting value in all these chatrooms. A link to frozen/deleted rooms would be useless anyway.