If you really want to, you could make a program (or shell script) which calls script writing to a timestamped "typescript" file (and in turn calling your real shell) and make that program your default shell in /etc/passwd.
There are a few pitfalls:
- you may have to add this program to
/etc/shells - doing this sets the
SHELLenvironment variable, which is used in various ways. Override that to avoid loops (and other misbehavior):
#!/bin/sh SHELL=/bin/bash export SHELL script -c "$SHELL" $HOME/consoleOutput_$(whoami)_$(date +'%Y_%m_%d_%H_%M_%S_%N').txt