dApp development question: can the number of wallets a person links to an app be limited?

EthereumEthereum
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self.ethereum
I have an idea for a dApp that I want to start working on but have come across one critical issue. The core of this app will rest on the user only being able to complete an in-app task once. The problem is that in my current way of thinking this would be accomplished by allowing the user to only link a single wallet and not allowing the user to change it. This seemed like an OK idea but what will stop the user from creating a new account and registering a different address? Then I thought, "well since I am in the financial space, maybe I could use SSNs?" but then I thought that other countries might not have those and that is pretty personal information and since the app wont be directly linked to any markets or banks etc this info would be otherwise useless and thus present a potential security risk. So my question is: is this a common issue or at least one that has been brought up before? Or should I abandon all hope?