Well, you can use the same email and username at different gambling sites but it is not recommended to use the same password across all sites. 99% chances there won't be issues in using the same passwords, but consider you are also playing at any untrusted new casino or there are any bad characters in some casino. They may somehow get your password and try to login on other gambling sites and may succeed if you have the same passwords on every site. Although this may not happen often, but why take risk for even 1% chance of this being tried by any scammer.
You said it well that Email/Username/Passwords should always be different. If you give one password for everything, there is no problem, but if by chance the password is leaked due to any mistake, then you will lose access to everything. That is why it is always better to keep the Username/Password different and if it is difficult to remember, then you should note it down in a personal note. This is the safest way to keep access to everything.
I think that the best way is to keep the Username/Password safe by changing it instead of taking risks. It is especially important to keep Username/Passwords safe on casino sites because we are moving forward with the modern world and getting involved in various types of casino games. If scammers get them, it will cause us to lose money and personal access. So we need to be careful and save them with different passwords so that the passwords are saved.