I've always wondered this too.
I assume NASA, being full of smart people, there's a really good reason (maybe many) why not. But it would be interesting to know those reasons out of curiosity.
There's a video online that shows the overall assembly sequence of the space station over the decades:
to "ship of theseus" the ISS would be all but impossible because of the dependencies between components.
I mean, lets just pick a random thing: how do you replace one of the central pieces of the truss?
How do you replace the Unity node?
Replace Zarya?
MAYBE you can pick off pieces like Kibo or Columbus... but not a lot.
Here's another way of imagining this. Think of the ISS like a multi-story building.
In a multi-story building you can't just go "darn, the third floor just isn't quite what I wanted, I want to slide it out and put in a new third floor"
ISS: Same thing.
EDIT: pointer to the GIF in question:
https://upload.wikimedia.org/wikipedia/commons/f/fb/ISS-assembly-animation.gif