But are these truly exceptions? Or are they the result of subtler rules French learners are rarely taught explicitly?
I don't know what the precise rules or patterns actually might be. But one fact that jumped out at me is that -mal and -nal start with nasal consonants and three of the "exceptions" end in -val.
No, like parent says, with many things in French, grammar and what we call "orthographe" is based on usage. And what's accepted tends to change over time. What's taught in school varies over the years too, with a large tendency to move to simplification. A good example is the french word for "key" which used to be written "clef" but over time moved to "clé" (closer to how it sounds phonetically). About every 20/30 years, we get some "réformes" on the topic, which are more or less followed, there's some good information here (the 1990 one is interesting on its own) : https://en.wikipedia.org/wiki/Reforms_of_French_orthography
Back to this precise one, there's no precise rule or pattern underneath, no rhyme or reason, it's just exceptions based on usage and even those can have their own exceptions. Like "idéals/idéaux", I (french) personally never even heard that "idéals" was a thing. Yet it is, somehow : https://www.larousse.fr/dictionnaires/francais/idéal/41391
Errr. French is _not_ based on usage but has an official rulebook that is maintained by L'académie de la langue française. Obviously nobody is coming after you if you don't respect the rules but there absolutely is a defined standard. This makes French useful for international standards and treaties because the wording can be very precise and leave much less to interpretation.
To my knowledge there aren't that many languages that are managed as officially as French is.
The Académie tried to codify what was used at the time (which varied a lot) to try and create a standard, but that's why there's so many exceptions to the rules everywhere : they went with "tradition" when creating the system instead of logical rules or purer phonetical approach (which some proposed).
There's a bunch of info on the wikipedia link about it, and how each wave or "réforme" tries to make it simpler (while still keeping the old version around as correct).
Each one is always hotly debated/rejected by parents too when they see their kids learning the newly simplified rules.
Recently, the spelling of onion in french went from "Oignon" (old spelling with a silent I) to "Ognon" (simplifying it out), and event that one made me have a "hmm" moment ;)
I've never heard of such a rule (am native), and your reasoning is fine but there are many common examples : cheval (horse), rival, estival (adjective, "in the summer "), travail (work, same rules for -ail words)...
I don't know what the precise rules or patterns actually might be. But one fact that jumped out at me is that -mal and -nal start with nasal consonants and three of the "exceptions" end in -val.