Default PATH setting - reduce to something more sensible?

When I recently inspected an 'strace' log and saw the huge amount
of system-calls done for a simple standard command (like 'rm') -
it's more than a dozen! and most lead just to ENOENT - I wondered
about the default PATH definition which is for my system
  /usr/lib/lightdm/lightdm
  /usr/local/sbin
  /usr/local/bin
  /usr/sbin
  /usr/bin
  /sbin
  /bin
  /usr/games
(here I'm omitting my own additions, '~/bin' and '.', and I separated
them, one on each line for a better visualization of the "problem" or,
maybe better, for the "questions".)

The above PATH components are for a terminal running under some
window manager, a plain console window will not show the 'lightdm'
entry (but I rarely work on plain consoles).

This raises a few questions, and someone may shed some light on the
rationale for above default settings... (and how to "fix" it best)

Why do I need 'lightdm/lightdm' in the user's PATH variable defined?
(That directory contains just one special script and one executable.)
This entry is what annoys me most; it also reminds me of systems that
have every program vendor add an own PATH entry for their products.
Would it be safe to just remove that (in my '~/.profile') from PATH?
Or can I make it vanish by some other change, to not appear in the
in the PATH first place? (Of course without destabilizing the system
by that.)

There's no files in '/usr/local/sbin' (on my system); no admins with
special tools desires.

I don't seem to use executables from all the 'sbin' directories; I'm
positive I need /usr/bin, /bin, and I've also installed some things
in /usr/local/bin. It seems to me that, as a normal user, the PATH
(and with it the path-search) could be drastically reduced. Is there
a method to only have them in the PATH when 'sudo'ing any programs
that require root privileges and the privileged programs in 'sbin'?

I mean, if I 'sodo' a shell I get - and I think this is sensible! -
only /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
(no 'lightdm', no 'games', and no personal settings) anyway, and I
seem to have those entries available independent of any parent
process's setting;  PATH=/usr/bin sudo ksh  will still provide all
the 'sbin' directories in the privileged shell's own PATH setting.

So my thought is, for the moment as a workaround, to edit the PATH
in the .profile, and _remove_ all 'sbin' and the 'lightdm' entries,
or just explicitly _define_ PATH without the spurious parts). (Or
would it be advisable to do that change in all the shells' .rc
files?) Or is there yet a better place to "fix" things system-wide?

(Or better not touch a running system? - but it looks so messy!)

Janis