A common use case for many token-based applications is that users that are first-comers to the crypto ecosystem lack ETH to pay for the transactions to manage their own tokens. A mechanism for allowing gas-free token transactions could help.

Consider an off-chain agent that accepts messages signed offline by the token sender, that submits transactions to a token contract that accepts such messages for triggering the transaction, by validating the signature (something akin to transaction sender abstraction). The signed message could also include a fee for the submitter of the transaction (also in tokens), to subsidise its gas cost.

Note that this mechanism needs to be implemented in the token itself, since the user may not have the required ETH to make an approval of his tokens to the contract that would be implementing this logic.