The hardware algorithm behind the security in Stockholm's subway

The whole telephone network used to work this way, and actually many of those relays (and even the mounting frames) look identical to their telephone counterparts. And of course those were derived from the telegraph network, which is where all this stuff was invented. Send simple signals very long distances, very reliably.

As telephones got into automated switching with relay-based logic, complexity dictated that the systems be able to diagnose themselves to some degree. It's cost-effective for fully half the machine to simply monitor and isolate trouble in the other half, as that increases reliability and serviceability to the point where a large system can still work.

Even today with solid-state everything, the individual parts are more reliable than relays or vacuum tubes, but there are more of them, and there's always pressure to cut down on the manpower required to maintain the whole thing, so self-monitoring and fault tolerance is as important as ever.

Reliable system design is almost never synonymous with newest-and-fastest-and-smallest. It means well-understood technology with well-understood failure modes, airtight logic to control fail-over and fault isolation, and the hardiest components you can find for the given environment. In tunnels with cables running along electrified track, spanning city-scale distances with a whole power grid and weather and stuff happening in parallel, relays are still a sane choice.