I've also used it to fool programs that refuse to go into interactive mode when their input is not a TTY, but that's more of an abuse of script's purpose.
bash: cannot set terminal process group (1661): Inappropriate ioctl for device bash: no job control in this shell
With script -qc 'bash -ic my_alias' /dev/null, the warning goes away! (Of course, the real solution would be to turn my_alias into a proper shell script, but this works in a pinch when you have old habits to abide by.)
Anyway, if you're only interested in replay inside a terminal, and you don't care about sharing the recordings on the web then reaching for script first is my recommendation. However, if we forget about the web part, there are still useful things for local workflow, like idle time optimization, pausing/stepping through recording and a single recording file instead of 2 (if you record timing info with script).
Thank you Marcin Kulik!