As a incentive to run a full node.
Full nodes secure the network too, why is there no incentive on the protocol level like the mining process?
Yes I agree, running a full node can be inconvenient for home PC users, at which point an incentive would encourage the user to continue.
Maybe Satoshi thought about it, but couldn't find reasonable way to add it to the protocol.
Satoshi imagined that mining would become specialized, but even he couldn't have predicted how mining would become such a big industry, totally separated from running nodes!