In a roundabout way this article captures well why I don't really like thinking in terms of "normal forms", especially as a numbered list like that. The key insights are really 1. Avoid redundancy and 2. This may involve synthesizing relationships that don't immediately obviously exist from a human perspective. Both of those can be expanded on at quite some length, but I never found much value in the supposedly-blessed intermediate points represented by the nominally numbered "forms". I don't find them useful either for thinking about the problem or for communicating about it.
Someone, somewhere writing down a list and that list being blessed with the imprimatur of Academic Approval (TM) doesn't mean it is actually useful... sometimes it just means that it made it easy to write multiple choice test questions. (e.g., "What does Layer 2 of the OSI network model represent? A: ... B: ... C: ... D: ..." to which the most appropriate real-world answer is "Who cares?")
Why shouldn’t we care about layer 2? You can do really fun and interesting things at the MAC layer.
> Someone, somewhere writing down a list and that list being blessed with the imprimatur of Academic Approval (TM)
One problem is that normal forms are underspecified even by the academy.
E.g., Millist W. Vincent "A corrected 5NF definition for relational database design" (1997) (!) shows that the traditional definition of 5NF was deficient. 5NF was introduced in 1979 (I was one year old then).
2NF and 3NF should basically be merged into BCNF, if I understand correctly, and treated like a general case (as per Darwen).
Also, the numeric sequence is not very useful because there are at least four non-numeric forms (https://andreipall.github.io/sql/database-normalization/).
Also, personally I think that 6NF should be foundational, but that's a separate matter.