I too have complained about this a few times in the past. My main pc has a bug that logs me out of everything periodically and forgets every password, regardless of what check boxes I tick. On my phone it occasionally logs me out, and I don't usually realise until I'm halfway through reading a long thread then face the endless finger swipe back to the top of the tiny screen.
I'd also like to see the block of links pictured at the bottom of each page...
Various thread where this has been discussed before:
Links top and bottom
hmmm... there was definitely another thread on this but I can't find it.
Anyway,
the answer to your request was that someone somewhere thinks that having those links is bad SEO. Back in around 2008 - 2010 website owners were spamming links to manipulate search engine rankings. It is not a factor any more, and search engines recognise the benefits of good user
experience and have removed the impact (positive and negative) the spammy links had.
Personally I still think that good user experience trumps SEO factors and consistent user experience between logged in and logged out modes would be better.
Mike