There is no easy way to save a chat session to a file.
Control-A does not work as expected in the chat window so your only choice is to drag over the entire chat session prior to control-c copy.
For example, lately 3v0 has been helping be with a few of my projects, and there are some things that he explains that would be good for me to have a copy of. It would be nice to be able to look back on his explanations. Being able to take a copy of the chat conversation would be very helpful for future reference.
Mostly what DerStorm8 said. When we help people it would be a good thing if they could copy the chat session and go back over it.
Here comes the other shoe. If it existed I might organize more formal session on various subjects. The chat could be posted to a thread and people who missed the chat could read it and people who took part could keep it as notes.
I have copied chat in the past. When one is learning from another individual, some instructions can go on for a period of and hour or so, more or less. Depending on how many conversations are going on at the same time. It is a plus to be able to go back and reference technical instruction or pointers.
I don't have "all the timers"(sic) but do have sometimers.