Yes, I think we're all familiar with the "But it's not logical" argument from the Lynne Trusses of this world. The problem with that argument generally, and here specifically is that language isn't about sharing propositions of formal logic. Interpreting other people's utterances as logical propositions makes for a briefly amusing diversion in a light drama but it's a terrible way to carry on a real conversation.
"It's like the Somme out there"
"How does it resemble the Somme?"
"I mean it's incredibly muddy"
"But I am in fact willing to believe that it is muddy"
The legal origin of this idea of an "exception that proves the rule" is fascinating, but the phrase has taken on a life of its own. You will notice that people are also content to say "third time is a charm" (there is no logical reason to believe that third attempts are special in any way) and "If a job's worth doing it's worth doing well" (likewise, a shoddy job may be the only economic or practical option) and many other phrases which can't be defended logically. They're not doing it wrong, these phrases aren't intended to be truthful statements about the world, any more than anybody thought exceptions /actually/ prove a rule.