Yeah, I like to review log file to see if I missed anything interesting.
The reason I do so is that in a heat of a battle I DO miss a lot of useful messages, even in a turn based game.
Therefore, ALL text appearing on a screen I would like to eventually end up in the log. Most of it probably not interesting, but I do not want to miss interesting stuff if there is some. Tutorial messages are interesting and useful. What's more important they show only once.
On a related note: if you include game timestamp (turn number) together with terminal messages/machine hacking results and also equip/unequip stuff, that could serve as an alternative way to tell if terminal is ready, how long till repair/fab and if it's been close to 300 turns I've been wearing that memory backup unit.