You are responsible for maintaining the security of your account.
The 14 day ban is, in part, a security measure intended to ensure that no further fraudulent activity occurs on your account.
You could also say that the 14 day ban is a way to remind you how important it is that you maintain a secure account.
There MAY be some other way that Riot can verify that you are the owner of the account, but Riot doesn't really collect much, if any, information that can verify who the actual account owner is. Therefore they may not have any way to verify that you are the original owner of the account.
There is a risk that if they would allow a compromised account to be reactivated, they could cause other fraudulent activities to be attempted.
They figure 14 days is a good amount of time for someone to notice that their credit cards have been compromised.