If you mean to ask what the incentive for me working on this: Because domain names are centralized in ICANN and I wanted to try to build something that isn't. Also, I just think it's an interesting problem.

The protocol stipulates that indexers just ignore duplicates. It's first come/first serve. It's a looser social consensus, but Ordinals have well demonstrated that even without miner enforcement, the benefits of social cooperation can incentivize correct behavior.

One of the nice benefits of loose social consensus is that we can use it to deal with squatters in a decentralized manner as well. Most decentralized means of identity usually just decide that squatters have to be lived with (think .eth, .btc, etc), but with Nomen we could actually set up a system where indexers could subscribe to Nostr events from trusted third parties that keep track of "illegitimate" claims, analogous to spam blocking lists.

This promotes self-sovereignty, because anyone operating their own indexer can pick and choose which parties they trust for "spam protection", much like choosing ad blocking lists in your browser.

It promotes decentralization because it allows handling squatters and name conflicts with "eventual consistency", i.e. network effects will naturally select for the most rightful owner.

Lastly it promotes good behavior. Because it costs real resources (mining fees) to register a name, and it's cost-free for indexers to ignore your illegitimate claim, simply HAVING such a decentralized system to handle squatters means that there is very little chance it will need to be used often.