It also costs a couple hundred bucks to run an Ethereum node. You are confusing running a validator and running a node, those are two independent things, just like mining and running a node.

Wait, to run a node (like, just keeping track of the chain), or to mine in a way that isn’t entirely ineffectual? Because the former doesn’t seem like the proper analogy to staking.

You can mine with a Raspberry Pi. It won't be profitable. But, you'll be contributing to the security of the network.

What is the impact of a miner on the security of the network, conditioned on the event that it never successfully mines a block? I would think it would be 0.

The probability that a raspi ever mines a block (like, if it were to start now, not if it was going since the network first started) is negligible.

Therefore, I consider the probability that a given raspi would contribute to the security of the network, or, I suppose equivalently, the degree to which it contributes, to be negligible.

The way I understand it, nodes help validate transactions in real time. They keep everyone else honest. Otherwise, whoever mined the block could inject whatever they wanted. Everyone on the network is validing transactions.

Sure, that's running a node. That's not mining. That's not analogous to staking. The analogy to staking would be mining. The analogy to running a bitcoin node would be running some variety of ethereum node, not staking.