shell config /etc/profile does not set $PATH

[Milan Hauth]

lsb_release -rd
Description: Ubuntu 16.04.5 LTS
Release: 16.04

apt-cache policy base-files
base-files:
  Installed: 9.4ubuntu4.7

grep -e PATH -e environment /usr/share/base-files/profile | wc -l
0

expectation:
/etc/profile should source /etc/environment to set the $PATH variable

reality:
/etc/profile does not set $PATH

scenario:
when chroot-ing from arch linux into ubuntu linux,
and running 'source /etc/profile'
then $PATH does not contain /bin:/sbin:/usr/sbin
which are needed to run 'apt-get update && apt-get upgrade'

... otherwise 'apt-get update' fails with
Unknown error executing apt-key

and 'apt-get upgrade' fails with
Processing triggers for cracklib-runtime (2.9.2-1ubuntu1) ...
/var/lib/dpkg/info/cracklib-runtime.postinst: 7: /var/lib/dpkg/info/cracklib-runtime.postinst: update-cracklib: not found
dpkg: error processing package cracklib-runtime (--unpack):
 subprocess installed post-installation script returned error exit status 127

only after 'source /etc/environment' all runs fine.

/etc/environment vs /etc/profile:
environment is for all programs, profile is only for shells.
but shells also need the $PATH variable,
so including environment in profile does make sense, at least to me.