It never increases any security but it will make privacy issues if the site got hacked,You can never know where our documents could be shared even it goes to dark web for selling.
SO people who gamble a lot won't share their details to gambling sites.
There is an opportunity to protect yourself and also your personal information, that you send to a gambling website. I mean the case when you only send your documents to well-known a very reputable sites, which will never sell or share your data on purpose.
What can you do is just put some kind of watermark on your scans of the documents, for example "special for casino name". It makes such marked documents less attractive to be sold, especially in case of hacking, data leaks, etc.