[Satoshi obviously understands human nature and planned Bitcoin accordingly. One of the mistakes he admitted was offering no reward for running a full node. People still do it with the best interests of the network in mind, but there are decreasing numbers of people prepared to do it for nothing. There would be an order of magnitude more nodes if people were rewarded for running one.
It was no mistake. The concept of a "full but non-mining" relay node is an aberration. Such nodes are precisely the sort of "trusted intermediaries" that bitcoin was supposed to get rid of. They do not add anything to the security of the network -- on the contrary, they are a gross violation of the protocol, and a huge security risk.
What Satoshi called "nodes" were the miners. Miners were supposed to mine for their own benefit (as users of the network) and for the fees paid by simple clients, who should contact them directly. Miners have incentives to validate and secure transactions on the blockchain, and serve all clients that pay enough to offset their marginal cost of doing so. Miners are prevented from defrauding the system by the proof-of-work and most-worked-chain-wins rules. In constrast, the "full but non-mining" nodes have no financial incentives to be honest, so one shoudl wonder what is their motivation for offering to "help" clients. There is no way of checking that they actually store or verify anything, so nothing prevents an attacker from cloning thousands of such nodes -- and scamming all clients that happen to talk to only those clones.
"Full but non-mining" relay nodes were invented by bitcoiners who were unable to compete with industrial miners, but still wanted to retain their control over the system, because they felt entitled to it. Non-mining clients should avoid them, and talk directly to miners (or relays that they cantrust are operated by miners). The sooner they disappear, the better.