Consider for a moment the seemingly unrelated case of clients storing data. A vault storing the PUT data doesn’t earn the fee the client pays to PUT data. But there is an ‘indirect’ benefit to the vault because clients doing a PUT involves recycling safecoin so the rewards for GET become a bit more likely due to slightly increased supply. So the vault benefits from PUT, but not directly because of the fee.
So maybe in a similar way, agents are not directly paid the fee for the mutation, but the fee goes to a ‘pool of rewards’ which the agent can access via some less racey mechanism. I think this is how it works, since a mutation is a PUT, but anyhow the idea is what I’m getting at, not the specific implementation.
It may be that a client wants ‘no condition’ in order to mutate their data. This requires no public keys. See Script - Bitcoin Wiki especially 2.4 Anyone Can Spend and 2.5 Freezing Funds Until A Time In The Future. There are cases where mutation does not depend on client permission (ie signatures).
It’s true that signatures will almost always be part of the mutation. But it’s incorrect to assume they will always require signatures.
To clarify, the group itself and the messages between the group must use each others signatures for secure messaging and consensus formation, but the inputs to the mutation do not necessarily need to include client signatures in order to mutate data (but usually will).