An example of this is this hidden file: .recently-used.xbel located in amnesia folder. To see, open Home/amnesia, press Cntrl+h, look for that file. The contents of that file logs recently used programs and files with names and timestamps.
There are many other logs for different activities and events, a simple look around can locate these.
Caching thumbnails, recent documents, terminal command history and the similar..
Why would Tails need to log all these things during the session?
Some are useful for bug reporting, but many other arent and are widely revealing of system activities.
Yes, a restart will wipe everything, but what about while in the session?
Can an option be made for Tails to be log free or normal where the user can choose between the two? Like run log free and if a problem occurs to re-run tails with logs to identify the problem.

Because it's useful and convenient, and does not conflict with our design goals.
I guess it may be possible to convince us to accept a good patch that implements this. But please, first document very well the kind of threats you want to protect against, and then think if/how the intended implementation really does :)