It is said also that "
It didn't happen after using a centralized exchange". The idea of this story is to warn people from uploading documents everywhere. But casino isnt "everywhere". Imo they are more secured that other places where people upload their documents. First thing that came to my mind are travelling agencies or rentals (the one that are not branded; some local with old cars, which foreigners prefer due to low price). People freely give them to copy documents or send by email. Those places are unsecured and should be avoided. Casinos imo are more protected from hackers. Moreover, for hacker, money would be a priority to steal.
Except what you wrote is also incorrect, even if your advice is alright. You are contemplating several things that have nothing to do with each other. Most people are dealing with travel agencies and rentals in person, unless they chose to do it otherwise, and in this case instead of digital uploads a physical scan can do. Unless they are for some reason doing extra work, and digitizing these scans, they are more secure than most digital solutions. As far as email document sharing, sometimes it is even official government locations that request that you send it this way -- they won't accept encrypted or even watermarked documents. But you can't compare things that one needs such as government-related stuff, or transport capability with something that is completely optional. Furthermore, your claim that "casinos" are more secure is completely made up. Most of these casinos, similar to CEXes, run on very badly engineered software that has countless holes. Furthermore, they do not have any strict data storage or retention practices. I doubt that there are many or any travel agencies that have the number of documents that a big casino or CEX has. Not even close.
The larger the company is, the closer control over the work of employees is.
This is not necessarily true, don't make unnecessary generalizations.
Casino, as a place that works with large amount of money, work with risk and have thousands and thousands of customers, chances that documents could vanish, and nobody would get caught or be responsible for that, are very low. As usually, nothing gives 100% guarantee and there is a place for exceptions. But I believe that casinos are not top places where users private data could leak easy.
You are again confusing things. Nobody needs to "vanish". An attacker does not even need to do a real hack of anything. They just need to convince one third world, lowly paid idiot employee that has sufficient access to give them to it. This can be done through coercion, persuasion, bribery, trickery, many methods. Stop defending casinos in this topic, as your defense is completely misplaced.

KYC is a scam, and casinos are very vulnerable.