no it doesn't. and you'd have to pay for names, which disqualifies it for mastodon like usage from the start.
Can you elaborate on how it doesn't? It ticks all of the boxes from your message.
Only the top level namespaces require a purchase. Names for services (e.g. james.mastadon.eth) are free. A live example of this is Coinbase which gives users (name).cb.id for free. Once your service claims a namespace you have full control over it.
ENS (https://ens.domains/) solves this problem rather elegantly. A single source of truth that is decentralized so any app can use it without trusting anyone. It wasn't around when Mastadon was being built unfortunately but is useful for developers of new apps and protocols.