Advantages

• 20 people living together in a remote village with constrained access, could, as long as they could get together occasionally to share network access via the "village wifi", and at the same time check the blockchain, could theoretically effect real economic payments over a long period, using such coins and transferring them as small files. It would be pretty limited due to denominations, and the collateral requirements (penalty bonds) would probably all have to be committed in advance here (effectively, locking up 100% of the value that could be transferred) to avoid needing any network/blockchain checks during usage.
• Secret agents and similar needing super-high opsec, not wanting any ability to network trace their payments at the time they are made. A small group of people could do the initial negotiation of the pathcoinstate files in a Faraday cage, exchanging messages between their computing devices (the funding utxo could be prepared in advance of this meeting, without yet broadcasting the funding). Later one participant can fund the coin, and all the others fund penalty bonds, in separate, disconnected Bitcoin payments. Then individual transfers can be done "sitting on a park bench" with no blockchain access, no network access, only a cheap computing device capable of comparing the transfer file with the state file and ensuring cryptographic consistency. A fanciful scenario perhaps, but it has some logic.