Is there any grammatical reason why non-identifying relative clauses are separated by commas or is it simply a convention?
No, there's no grammatical reason why there are commas around non-restrictive clauses. Commas aren't controlled by grammar in English. The distinction is in the pronunciation of the two types of clause. This difference in pronunciation (intonation curves, mostly) is often expressed by commas or dashes. But no real English grammar rule refers to punctuation, spelling, capitalization, or spaces. That's just orthography, which isn't language, but rather modern technology. Sort of modern, anyway.
The reason for the difference in pronunciation, though, is precisely to distinguish the types of clause. Restrictive (integrated, identifying) relative clauses are just modifiers, and very common. They're the norm and don't need any marker. Non-restrictive (supplemental, non-identifying) relative clauses, however, are essentially separate utterances on a related topic, rather than being part of the main sentence itself.
As such, non-restrictive clauses are normally delivered with more flatted intonation (in a lower tone of voice) than their antecedent noun phrase, suitable for obiter dicta like these. The transition to this flatted intonation stretch is the first comma intonation, and its end is the second.