Should "su" change the USER environment variable?

[bob%ucla-locus at sri-unix.UUCP]

From:            Bob English <bob at ucla-locus>

Do you really know how to do a "layered login"?  If you invoke login
from the shell, it will overwrite /etc/utmp and the other person will
appear to be you forever more.  This is particularly interesting when
you log on as who ( or date or whatever).

--bob--

P.S. This is the case for 4.1bsd and v7.  If someone has fixed this, I
wouldn't mind hearing about it.