Yes, so much this. It used to be that important logs (filtered by severity and keywords) were even continuously live-printed by a line printer, so that there was always a current paper copy of the really important stuff for forensics.
See e.g. https://www.youtube.com/watch?v=FiEGoVzmyvs but dot-matrix was also used and at least a little less noisy.
tsch! tsch! tsch! tsch! "Ah, someone is trying to login as root again"