Is there a reason why you can't have a random topic sort on a block fed from existing topics? 

Its been this way since 4.0. I believe it was explained because its pretty resource intensive. But you can make your own block with a custom query that is random just remember that blocks are cached.

Ah, OK. Thanks for clarifying. I was sure it used to be there and had this idea to create a page with a feed of maybe 20 topics pulled from my 15 years of archives. 

It was there in 3.x but hasn't been around since 4.0 was released.

We support "random" supporting in some blocks but it is indeed very resource intensive. I wouldn't use it on a larger board.