This is quite smart and would be possible. It would be interesting to see how the casinos would battle an influx of fake documents... This would most likely create another completely opposite industry (e.g. software to detect fake documents).
Maybe falsification of documents to verify gambling accounts can happen. Still, it won't happen forever because the casino will look for ways to prevent it. Maybe later, there will be face identification of each gambler so that the casino will know that the account owner is really valid. We have seen that some exchanges are already doing face verification and this may also be implemented in casinos that want to have real members with the documents they have.