Yes, this has been done before (on the runet, mostly), we just made it easy to use (no accounts, no balance, lightning payments).
The main use case I'm seeing is using services requiring phone number verification without giving them your real one. For example, if you go ahead and create an account on Twitter you'll get blocked within two minutes until you also give them your phone number, despite the registration pretending it's not required (because once you signed up, it's easier to trick people into giving up yet more information than asking for it upfront).
I would incorporate that use case into your website copy because it’s really compelling
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