On reflection I was incorrect to mention Napster, which (at least in its most-popular incarnation) was still centralized for indexing and searching, with P2P only for bulk file data. Please pretend said "Gnutella" alone.

> The analogy is [the P2P application] on a LAN.

The analogy is the P2P application where regular clients can only discover a Special Master Client that must be running on a fixed IP, which only permits connections if you have credentials for a user-account arranged in advance.

In each case, the system's centerpiece feature is being voided, but that feature is different between them.

1. For "Blockchain", the centerpiece is unrestricted participation. (Other decentralization is an indirect effect.)

2. For P2P file sharing, the centerpiece is how nobody needs to run an expensive/vulnerable central server, but it wasn't a contradiction in terms to have a private peer-network.