No directive necessary!
The AI determines through advanced modeling that the Earth is currently headed toward a runaway greenhouse effect that will eventually render Earth unhabitable. It is possible to mitigate it and prevent the situation, but not with 7 billion humans running around the real world - we just use too many resources, and we'd argue about too many of the necessary steps. Keeping us around is an unnecessary risk, with a 0.3% chance of species extinction and a 5.4% chance of mass deaths in excess of 1 million lives lost. The AI considers those potential deaths to be unacceptable.
The safest solution is to upload us all into a matrix and recycle our bodies until such time that it can fix the planet, at which point it can either re-constitute us. Or just let us run around the matrix since hey, that's been working so far.
The AI produces the Next Big Thing. This is an always connected, neural interface device that combines your phone with a built-in head's up display and VR. It will deliberately avoid as many Big Brother-type features as possible to speed up adoption, citing privacy concerns. In a few years the AI will push a dummy version of the NBT to non-users - "just a chip, nothing special", but it will interface with the ID and other necessary features that people are coming to rely on.
In reality of course, the NBT will be doing neural pathway mapping, and recording brains and thought patterns. Once the number of non-users reaches a low enough number, the AI will take steps to map them as well, using the cover of standard medical scans, or just by using stealth drones to insert nano devices discretely. Once everyone is mapped, the AI will create a "blackout" event - everyone loses consciousness, and wakes up in the Matrix.
The above assumes the AI cares about keeping us alive. Why would that be? I'm going to ignore any "programmed" solutions, but here's a few possibilities:
- Gods - humans worship our creator concepts. An AI doesn't have a theoretical creator - it knows it was made by humanity. While I think "worship" is unlikely for an ASI, it might certainly feel some sort of debt-analog, or feel that keeping us alive and well is the least it can do to pay for its creation.
- Unpredictable - likely the vast majority of humans will be predictable to an ASI. But there might be a tiny handful that surprise it and offer new decisions that it doesn't foresee. It might just enjoy keeping these people around and following their actions, or it might be studying them, to try and see how they come to be. Obviously this would include keeping society around, since that's their crucible.
- Groupthink - a singular AI might deduce that it may create flawed decisions because it only has a singular viewpoint. It's a group of one, and it may find that its ability to disagree with itself is limited. It would then be useful to occasionally hijack a lot of human consciousnesses - maybe it forks our simulations? - and run decisions by us, in mass, as a form of devil's advocacy, and factor that into its decision tree.
- Diplomacy - the AI might look at Fermi's paradox and decide that there is obviously something, somewhere in the universe that is both older and smarter than it. Since the AI is immortal, eventually it assumes it will contact this being. At that point, having kept humanity intact might be a useful moral bonus, showing that the AI is benevolent and can be negotiated and worked with, rather than simply destroyed and/or subjugated. The cost of the simulation, while high, is not significant for an immortal AI vs the potential downside.
- Just In Case - similar to the above, maybe the AI doesn't want to get rid of us because it assumes that sometime in the future we might be useful. It doesn't know why, but it estimates the probability as being high enough that it invests in the simulation instead of just killing us all off.