Why it doesn't work?
pkexec does not allow you to run graphical (X11) applications. From the man page:
The environment that PROGRAM will run it, will be set to a minimal known and safe environment in order to avoid injecting code through LD_LIBRARY_PATH or similar mechanisms. In addition the PKEXEC_UID environment variable is set to the user id of the process invoking pkexec. As a result, pkexec will not allow you to run X11 applications as another user since the $DISPLAY and $XAUTHORITY environment variables are not set. These two variables will be retained if the org.freedesktop.policykit.exec.allow_gui annotation on an action is set to a nonempty value; this is discouraged, though, and should only be used for legacy programs.
As stated in the man page, you can make it work albeit I really don't know if this is somehow dangerous or recommended.
To enable gedit for example you can create
/usr/share/polkit-1/actions/com.ubuntu.gedit.policy with the following content:
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE policyconfig PUBLIC
"-//freedesktop//DTD PolicyKit Policy Configuration 1.0//EN"
<message>Authentication is required to run Text Editor</message>
pkexec gedit should work as expected:
As you can guess, this will only make
gedit work. In theory, if you added
allow_gui to "org.freedesktop.policykit.exec" (the default action) this should work for all applications, but in my tests I got the same result as yours.
Why is pkexec preferred?
Here you can find a discussion about the strengths of