I think the "people, places, things" got injected from Al-Anon.

Instead of powerless over alcohol, I've heard them refer to being powerless over people places and things.... and possibly that's where some AA's who thought it sounded cute began to use it.
This is actually a very interesting topic. A course of mental gymnastics.
Our BB has no references, at least in the Program of Recovery section about being powerless over people places and things. Someone may be using it in the story section if it's to be found in the BB.
I remember early in recovery being confused about this sort of thing... and that's one of the places that a very wise and well read (BB) sponsor can come to aid.
To be powerless over people, places and things... if one really wants to think it through... one would have to be to be dead.
I may be powerless over the need to go to the bathroom... however, most always, I've been able to control that need with planning, patience and will power... so that I could choose the place and the thing that I was going to use for a toilet.
And, of course... if I stop eating and stop drinking liquids... I could control the need.
If the world was powerless over people, places and things... I wonder why we would have Air Traffic Controllers?
Wouldn't Air Traffic Controllers... have a reasonable amount of control over outcomes and results?
Sure... they couldn't maintain 100% control... however their awareness, actions and efforts would be well welcomed... And, would have much to do about results. 99.99% of the airplanes don't crash!

Without the Controllers... the results would probably be just the opposite... 99.99 percent would crash! In that case... I'm sure that we would hope that God really was the pilot that was flying all the planes all the time.
Also, if we are powerless over people places and things... as some would suggest that we are... we would not be accountable nor responsible for anything.
We couldn't pick up the phone. We couldn't call for help. We wouldn't go to meetings. We couldn't be responsible enough to take our steps and recover. We could say "Well God... don't look at me! I had nothing to do with it! Remember... I'm powerless!!! It's all your fault God! Those are your wrongs and your aments... so don't bother me with your stuff!!!
Dallas