People have to trust that their money is safe within a community. Requiring each community to provide its own local infrastructure will be both inconvenient and introduce friction. It will also drastically reduce security: if a community has only 10 computers running validation, it’s much easier to undermine. You can, for example, blow up all 10 computers and make it forget who owns what. This is a problem for Proof of Work and Proof of Stake as well.
That is why each community starts out using validators on the larger network. These validators collectively maintain a ledger about all coins in all communities. However, the ledger is horizontally partitioned down to the coin! Each token is a non-divisible entity that is watched by several computers on the ledger.
There are some positive theoretical results about decentralizing the ledger for a crypto-currency.
An academic paper from 2009 shows that even if the network maintaining the ledger is partitioned into different subsets (referred to as sharding), the probability of a double-spend quickly approaches zero as the number of nodes in each subset grows, becoming extremely small when each subset has 30 nodes. There is no need to have the whole network watch every coin or process every transaction.
Our approach is similar to the one SAFE Network uses in that it uses Kademlia to choose the groups of validators to watch over each token, and each transaction. The latter group is unpredictable in advance, but the former group is predictable given the token ID, so we also implement “churn”, effectively reassigning validators to different groups from time to time in a process they cannot control. This, along with other measures like strong cryptography, prevents a whole host of attacks. The main attacks to be mindful of in that framework are eclipse and sybil attacks.