So, the pip-boy device the PC wears on her arm acts like a computer in some respects, keeping track of her skills, stats, medical condition (presumably somehow monitoring her life signs since it IS connected to her flesh, at least)... it can also be used to play audio tapes and (in Fallout 4) video games and can be used to access or unlock some things (reason for being invited to Operation Anchorage, e.g.).
But if the Pip-Boy only ~catalogs~ your inventory.... first of all, how does it know what you have in your inventory? Do you manually type it in?
"Let's see, I just picked up a stimpack, a box of Fancy Lad Snack Cakes and a 10mm pistol holding three rounds" .... click click click (typing)...
But aside from that, when you "access" your Pip-Boy is when you are able to switch weapons, put on armor, or take meds/stims. Without accessing the Pip-Boy (unless you hotkey, of course ;D) you can't do that.
If you look at your character model, you will only see the equipped weapons and armor.... you don't see a backpack with four rifle barrels jutting out the top and a string of StimPaks tied together dangling off the end of the pack, or two full sets of leather armor bulging at the seams. No, all you see is the equipped armor and weapons.
To some degree (perhaps entirely, making this post moot) it's a meta-gaming thing.... but from the ~character's~ point of view... and the point of view of NPCs who see the character.... where ARE these items that we think of as "in my inventory"?
One idea that sprang to mind came from the movie Ultraviolet (Mila Jovovich). Yes, it's not exactly high cinema, but it was a fun little romp, I thought. Anyway, they had in that movie a thing called Flat Space technology which basically acted like an old-school D&D "Bag of Holding", letting you carry around big things in a sort of dimensional pocket.
In the movie, there was a suitcase that acted as an interface only, and a young advlt was floating horizontally in a solution inside. Or they'd have a simple wristband or something similar (belt buckle, I forget, but small) and a katana blade could be drawn out from it, even though the blade was not previously visible. In one scene a scanner displays a holographic image of Mila's character, and says something like, "Illegal weapons found ----- Many." and the image shows row after row after row of weapons, not visible to the naked eye but "stored" in the Flat Space container.
There's even a scene where she is holding a weapon and ammunition is flowing out of the Flat/Folded Space device on her wrist and into the magazines of the gun, giving a rationalization for the "infinite ammo" feature seen in many action movies.
Anyway, while the technology certainly seems more advanced than anything else in the Fallout universe, it looks like it would be a nice tidy way to explain how we can pull up our wrist and yank out an entire set of armor and an assault rifle from thin air.
Perhaps the technology is tied to the Pip-Boy and cannot be manufactured any more ---- would go even further toward explaining how seeing someone with a Pip Boy on her wrist is a strange sight and one that indicates that the person has power.
Or should I just not be thinking about how my character miraculously pulls a Minigun out of thin air? "La-la-la-la, neveryou mind how I did it!"