There is nothing in the NEC directly saying that you can’t do it. I believe the term that INDIRECTLY says it is the the SCCR of the equipment must be determined by an “approved method” (words to that effect, I don’t have my NEC here). Then somewhere else they list the approved methods, being testing, or the series listing process in UL508A Supplement SB, or a PE letter attesting to the validity of the series combination.
So that is what stops contractors and end users from doing it on their own in the field when some buyer slacks off and fails to include a PROPER level of SCCR in the call for bids on the equipment. Because really, it’s NOT DIFFICULT to attain a decent workable SCCR, it just requires selecting combinations of parts that have ALREADY BEEN SERIES TESTED AND LISTED TOGETHER, instead of buying the cheapest part you can find for any component and kicking the can down the road.
And circling back to the CL fuse issue, they CAN AND ARE used in this process all the time, but they must be TESTED AND LISTED with the components involved for it to be valid (other than the PE option). Most UL/ETL/CSA listed components will have gone though that process already, so the people building the panel just have to find that data and document it when applying their UL label. But it does mean that the list of components they can use TOGETHER is more restricted because, for example, a Square D or Eaton or AB contactor will not be listed in series with a cheap Overload relay that they got from some Chinese supplier that is technically UL listed, but never series tested. Simple little rules like that.