Several languages have this. Spanish has the Real Academia Española (RAE) and French has something similar.
But they're not generally in much of a different position than a dictionary is. If the people start using the language in new ways they have little recourse other than to accept it and amend their rules. If they refuse they'll look antiquated and people start to question their influence.
They certainly do have influence of course, but the ultimate authority is the people who speak the language in the end.
People always think the académie française is antiquated because it doesn't like new anglicisms (old ones are fine though) and sometimes invents words. But in general language standardisation will always be seen as antiquated because it needs to lag behind at least a decade, otherwise things get standardised that are just a fad or where no general consensus has been found.
Do they monitor your private messages and fine you for typos or do they just codify the language which is taught in schools and used by the authorities? If it's anything like German language regulation then it's the latter and the way people actually talk and write slowly is adapted by the language regulations.