The arbitrariness of grammar rules you mention is nothing compared with the standardization of spelling. I see a connexion between the motivations behind both - pedantry.
In both cases, standardization of spelling and grammar, they have the role of streamlining communication. Try reading posts that have non-standardized spelling. If the spelling is phonetic based, you have to pause and think how the word sounds. Awkward grammatical sentences are hard to parse.
There is a point to standardizing these things, though, past a certain point, it's a bit absurd and your point stands.
Regarding phonetic spelling, non-phonetic spelling such as is found in English is unusual - the idea of a French or German spelling bee is incoherent. Even though a book such as Le Morte d'Arthur is unfamiliar at first, the spelling differences disappear pretty quickly once an English speaker's attention is focused on it.
