Signatures show up when users aren't logged in exactly the same as when they are. Archive websites usually aren't logged into accounts, however (as you can see following the link), the website picks them up fine. Are you sure you don't have any extensions/scripts running on Bitcointalk?
I think it has been that way for a long time and it is at a lot of forums. I believe some forums do it to cut down the bandwidth consumption that search engine bots take up, they have no obligation to show your links and you have to be happy they allow it at all
For the amount of bandwidth it would save it is questionable if anywhere would do it for that reason at all. I expect that, if it were in place, it would be to prevent spam back links from promoting a website in search rankings.