Exactly.
The AR-15 is in a league of its own regarding lubrication, due to the fact that a huge gust of crud is blowing into the action with each shot.
Add to that the fact that a whole bunch of .223 can be fired in fairly short order from one rifle, and the resulting carbon, soot and residue buildup rapidly becomes an issue.
Grease will work if you just want to fire a few rounds per session, with degreasing between sessions...and then only in warm weather.
CLP has the wonderful quality of being able to dissolve and 'float' fouling inside the action. This means that even though the lube really does catch the crap, it redeems itself by breaking it down and keeping things slick.
Add a big dose of powder fouling and soot to your average grease, synthetic of otherwise, and you soon have lapping compound! Rub steel and aluminum together in the presence of this gack and watch those parts shrink! Yikes.
That's why grease isn't used much on AR-type rifle actions.
I do indeed grease the pin-holes on the lower, however; the hammer & trigger pins revolve in their holes, and since this is a low-gunk location, I find I cut friction the most with Militec grease. So I use it and replace the grease monthly, or more often if shooting excessive amounts of ammo.
Nothing on the bolt carrier needs greased, although since Militec's oil and grease are said to play nice together perhaps you could coat the bolt carrier's action rails, if that makes you happy. Definitely do NOT grease anything inside the BC. It will carbonize!
I use their Firepower CLP on everything from the bolt lugs to the gas rings to the action, and also the external parts as a protectant. Works great.