There are three drivers for the list:
One is a basic ISO 17025 requirement that the test records have enough detail to be able to re-produce the result (e.g. if challenged, or design update etc). This is done through identifying manufacturer, make/model, serial number, photos and critical parts list, circuit diagrams, spec sheets for certain parts and so on.
The second is that IEC standards normally have a clause that requires certain parts to be certified components, and some clauses also make reference to specific attributes. A list of critical components helps to provide evidence of meeting these requirements (in the body of the report, you can just say, see the critical component list, rather than listing each part in the relevant clause).
The third is that if product certification is involved, the factory inspectors will use this list (and the photos, spec sheets etc) to confirm the product has not changed. The most popular by far is NRTL but there are other schemes.
None of this should imply parts listed are special in the sense only changes to those parts trigger retesting or evaluation.
Regardless of what is on the list, for the manufacturer any design change should trigger at least an internal re-evaluation of standards compliance, which might range from a single sentence - "obviously no effect" - through to detailed re-testing.
If the device is under product certification, a separate decision has to be made whether to report the change to the agency. The list might influence the decision, but keep in mind other changes can also trigger re-evaluation (for example, a software change or "non-critical" secondary part change might influence transformer loading).
For CB reports, there is no obligation to report changes. CB reports are only a stepping stone to product certification. They keep the lists also with an eye to facilitate the eventual certification process/factory inspections. But strictly speaking this is not the real list used for product certification.