Interesting. I guess the only weakness I can see is that there is no way to know that a request genuinely comes from the person you think is requesting it.
On the one hand, that is down to how you send and receive the URLs. On the other hand, it doesn't make it clear that you should pay attention to that and that it provides no identity authentication.
That's a really interesting perspective. I thought of the anonymity piece as a feature more so than a limitation. For example, you want to share something between two people, but want to "burn after reading". This way no one can associate the message to the two users or get access to the contents. The requester can always clear their local storage of the key. For example, it would be really useful when sharing information between a whistleblower and a journalist. Identity comes from the medium you share really in this case.
On the one hand, that is down to how you send and receive the URLs. On the other hand, it doesn't make it clear that you should pay attention to that and that it provides no identity authentication.