The short answer is that it keeps the system fully 'trust-free' (permisionless), and that it, in the same way Bitcoin incentivizes hashing random numbers, incentivizes routing nodes to form efficient networks (networks which race to get fee paying data into blocks while minimizing hops).

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Routing nodes will lose to competitors if another routing path on the same fee is included in a block. They also diminish the 'work' in the transaction (which overcomes the threshold to make blocks) by adding hops - so it's only worth it to add hops in order to 'win the race.' All nodes in the path have an expected value on the fee, but the further into the chain of hops, the more that diminishes.

In a technical sense, it isn't necessary to then reward those routing nodes to keep the anti-Sybil property for the routing network itself, but it does give other nice properties related to trustlessness and network provision.

1. Data pays no fees, routers get no rewards

Assuming data is published to a shared medium which requires some threshold of "work" which stems from the data, then even just the act of including that data into your medium becomes more difficult the more hops it accumulates. You then of course rely on trust assumptions to fight spam.

2. Data pays fees, routers get no rewards

If you use some measure of cost to create data, you can handle spam, and that cost determines how much work the data carries with it and thus how likely it is to be included into the medium (trying to be very general here, but in the linked article that medium is a blockchain). The trust assumptions here rest with the routing nodes 'doing their duty.'

3. Data pays fees, routers get rewards

This is the model Saito has - it removes trust assumptions for users and routers as if one tries to 'scam' the other (either a Sybilling user creating fake data, or a Sybilling router creating fake hops), the native money can be leveraged to create recourse without an authoritative audit or punishment - purely economic.

Do you want your transaction fee to pay for mining, or do you want it to pay for the servers that run the network? If it pays for mining, who pays for the servers that run the network?