That would seem to be a good requirement and I do think that should be stated clearly in the code, but as you know, it is not. AFAIK, the closest general statement to stating that is ye old 110.3(B).
If you are looking for explicitly stated, you are correct. However, it is inferred throughout Code. Half the problem with Code is it is written for the most part in pseudo-legalese form, as opposed to explicit, direct, concise technical form. I surmise if written in the latter form, Code could be reduced to roughly half its current size and less misunderstood.
I would partially disagree with that (because you did say "most cases"). ...
Quit using my own 'brand' of textual logic against me... :angel:
... Conductors and panelboards are the only things I can think of that must be protected at their rating by an OCPD. Of course many things are allowed to be protected at somewhat over their rating like motors, phase converters and transformers. Switchboards and meter sockets have no requirements to be protected by an OCPD of any size. Then there is the issue of equipment that does not have a specific NEC article: Where is the OCPD requirement for those?
I don't want to get into specific requirements for each and every type of equipment, but here is where some of the ratings are inferred. For example, switchgear is typically used as service equipment. While Article 408 don't require OCPD protection, Article 230 requires it to be rated not less than the ampacity of the service conductors. Minimum meter socket rating is typically specified by the utility provider (yet what of customer-owned meter sockets?). Then we have items such as a 15A receptacle permitted on a 20A-rated circuit.
You are in error regarding motors. Yes, SC/GFP rating is greater than conductor rating, but you have to consider motor circuits have additional protection in the form of overload protection. It is generally limited to 115% of rated current, while conductors must be sized at 125%.
Phase converters and transformers fall into the category of non-load equipment, as do inverters, charge controllers, and other distribution and control equipment.
The easiest way to look at the required rating for anything that is not a source, OCPD, or load... and not specified explicitly... is as if it is a conductor. This equipment must have a current rating not less than the minimum required ampacity of its circuit conductors... but there will always be those items which fall through Code 'cracks'.