Anonymous users can't see the live discussions page

It's not a bug. The page reports the threads that have been commented on since your last visit, and you must be logged in to get that. The block gives the best you can get for unregistered users, which is the configured number of the most recently commented threads.

Not unless you program. If you can wait until the weekend I can sort of expand the block into a page for you...totally unsupported going forward.

I failed to achieve this with views, so I'd like to have such functionality, if possible. Some means to administer and configure the page would be great too.
Just for the record - there's a workaround - using "insert block" module it's possible to provide live discussions page for anonimous users.

Do you understand what I have offered? The fact is, my offer would give no more functionality than the block does now, nor am I offering to support such a change.

there's quite a difference in what was requested and your offer, so may be I was mislead...
if that's the only option, then I'll follow Lukas2000 at #4
live discussions + insert block already does what you offer, so there's no need to waste your time on this

there's quite a difference in what was requested and your offer

Yes, there is. Sorry if you feel misled.

I can sort of expand the block into a page for you...totally unsupported going forward.

That means no new comment count, which is the only real functionality the page has over the block. Also, the size of the page is self-limiting because it only looks at comments made since your last visit. To provide that for anonymous folk would require reading the session or a cookie, and other conditional stuff that is more work than I care to do for GPL functionality I really don't need. Or I could read the variable that sets the size of the block and, again, there's no value add over the block. There may be value in knowing the author of the nodes...