So yes, you really do have to slog through nearly 50 templated 'cases' before the backstory really sets in, and Michael Emerson becomes both the chilling and warm heart of the show.
Like others here, I have been surprised how well it holds up, with several of the episodes dealing with topics that are now current but were pretty much absurd at time of transmission.
Seeing it now the show also has some pretty fun foreshadowing of llm technology like an episode where they anticipate the idea of "ssd streaming" (running a model slower when you don't have enough memory to fit it all at once), at least this is how I interpreted it to make the connection.
And there are many others connections that now can be made thinking about llms vs the machine
Oh and they also anticipated the openai incident where models started using random stuff as external persistent memory across "sessions"
1. When Finch is out playing hide and seek with the machine.
2. When the machine is apologizing to Finch, telling him that it did its best.Just your last clause was a weird one, if you do watch all four seasons. This is a tiny bit of a spoiler, but the problem was closely related to what you say. They didn't spend much time AT all in the "transition" to an AI infested world, but instead, well, skipped A LOT.