Under relatively normal wear, the only parts that should be replaced are the crystal, mainspring, and rotor. That's 3 wear parts, not exactly a "ship of theseus".

If something is broken, sure. It might need replacing. But that's rarer, I think, than people realize, and rarely is it more than one or two parts of the movement.

I recently repaired my great-grandfather's pocket watch and the only replacement necessary was the mainspring.