Technically FLP impossibility only applies to deterministic algorithms, not randomized ones, otherwise no consensus protocol would work. So you could imagine a complicated technical solution that could work (eg. treating everything as a big Raft cluster and using Raft's membership changes every time a device is connected / disconnected).
In practice the solution is to realize that failures are rare (especially compared to events like the soldier simply misplacing the card), and to have a trusted human available to resolve any issues that do occur.
These instructions are not for the Neural Engine. That is a separate hardware block outside of the CPUs. Apple refers to this feature as "AMX" in their marketing documentation.
While AMX could be used for deep learning in a pinch despite the lack of support for common formats like fp16 and int8, I suspect Apple had some other use cases in mind as well. For example, 64-bit float support is expensive and generally useless for ML. However, they are useful (though not necessarily required) in problems such as bundle adjustment that may appear in the context of frameworks like ARKit.
Most recent tape standards have multiple "bands" and "wraps" placed in parallel. The head reads only one wrap at a time, so it takes many passes to read the whole tape. For example an LTO-8 tape has 52 wraps each within 4 bands, requiring 208 passes to read completely.
In practice the solution is to realize that failures are rare (especially compared to events like the soldier simply misplacing the card), and to have a trusted human available to resolve any issues that do occur.