I would argue they make the code less readable, merely because they are not the original names. I certainly had no idea what "set -o errexit" did—I've never ever seen it in the wild and it doesn't sound familiar to me at all (and I've done a lot of shell scripting).
But "set -e"? Oh yeah, I use that all the time. It also has the benefit of being the same name as the command line option. That's especially useful for "set -x" which I use all the time when debugging bash, especially in the form "bash -x myscript".
I would never say "tar --extract --file" either–it's just not done.