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.
Some people still do falsification of documents because some casinos' security isn't tight yet regarding this matter. This is the reason why some underage people are able to make an account despite the age limit stated on the TOS of the casino. Although most likely in the future this will also be resolved since the technology is now advancing continuously. Precautionary measure such as KYC can limit the illegal activities that could be done inside the casinos. It also serves as a good way to verify the identity of the person making an account, but as of now there are loopholes such as the aforementioned that needs to be addressed.
Some exchangers are indeed doing face recognitions before you can successfully make an account. This is to verify that you are really the holder of the identification card and it is not just stolen or bought from someone. This might be implemented in casinos too if they will prioritize security and exclusivity of their site to those who can only pass the requirements needed to open an account.