There _sort-of_ is. You can pull from registries other than Docker Hub (these can be run by anyone with the will and resources to do so -- GHCR is a popular one), though these may have their own usage restrictions.

You can run your own following Docker's own guide here[0] if you'd like. It's not peer-to-peer in the sense that the lines between clients and servers are blurred, as with torrenting, but it allows for a distributed registry architecture, which I think is the part that matters here.

  [0] https://www.docker.com/blog/how-to-use-your-own-registry-2/