As I understand it, according to the original plan, ALL of the wallets were supposed to be full nodes, so naturally there was not provided any reward only for that. Moreover! All of the nodes (wallets) were supposed to be MINERS as well! And as miners they would have gained the reward!
That's not entirely true. I'm not sure what security features were supposed to be in place with regard to Satoshi's reference to "Simplified Payment Verification" in the whitepaper. Maybe fraud proofs along the lines of what Core developers have proposed, or maybe he did not foresee that miners would try to change protocol rules from under users. See here:
8. Simplified Payment Verification. It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he's convinced he has the longest chain, and obtain the Merkle branch linking the transaction to the block it's timestamped in. He can't check the transaction for himself, but by linking it to a place in the chain, he can see that a network node has accepted it, and blocks added after it further confirm the network has accepted it.
It's easy to see how a user could be attacked this way. By verifying block headers, he can tell that miners have included in a block and further that the block has been confirmed. He can't verify that this blockchain is "Bitcoin."