The main short term danger from AI isn't how good it is, or who's using it, but who isn't: governments.
This impacts every aspect of our interaction with the State, beginning with the ludicrous way in which we have to move papers around (at best, digitally) to tell one part of the government something another part of the government already knows. Companies like Amazon, Google, or Facebook are built upon the opposite principle. Every part of them knows everything any part of the company knows about you (or at least it behaves that way, even if in practice there are still plenty of awkward silos).
Or consider the way every business and technical process is monitored and modeled in a high-end contemporary company, and contrast it with the opacity, most damagingly to themselves, of government services. Where companies strive to give increasingly sophisticated AI algorithms as much power as possible, governments often struggle to give humans the information they need to make the decisions, much less assist or replace them with decision-making software.
It's not that government employees lack the skills or drive. Governments are simply, and perhaps reasonably, biased toward organizational stability: they are very seldom built up from scratch, and a "fail fast" philosophy would be a recipe for untold human suffering instead of just a bunch of worthless stock options. Besides, most of the countries with the technical and human resources to attempt something like this are currently leaning to one degree or another towards political philosophies that mostly favor a reduced government footprint.
Under these circumstances, we can only expect the AI gap between the public and the private sector to grow.
The only areas where this isn't the case are, not coincidentally, the military and intelligence agencies, who are enthusiastic adopters of every cutting edge information technology they can acquire or develop. But these exceptions only highlight one of the big problems inherent in this gap: intelligence agencies (and to a hopefully lesser degree, the military) are by need, design, or their citizens' own faith the government areas least subject to democratic oversight. Private companies lose money or even go broke and disappear if they mess up; intelligence agencies usually get new top-level officers and a budget increase.
As an aside, even individuals are steered away from applying AI algorithms instead of consuming their services, through product design and, increasingly, laws that prohibit them from reprogramming their own devices with smarter or at least more loyal algorithms.
This is a huge loss of potential welfare — we are getting worse public services, and at a higher cost, than we could given the available technology — but it's also part of a wider political change, as (big) corporate entities gain operational and strategic advantages that shift the balance of power away from democratically elected organizations. It's one thing for private individuals to own the means of production, and another when they (and often business-friendly security agencies) have a de facto monopoly on superhuman smarts.
States originally gained part of their power through early and massive adoption of information technologies, from temple inventories in Summer to tax censuses and written laws. The way they are now lagging behind bodes ill for the future quality of public services, and for democratic oversight of the uses of AI technologies.
It would be disingenuous to say that this is the biggest long- and not-so-long-term problem states are facing, but only because there are so many other things going wrong or still to be done. But it's something that will have to be dealt with; not just with useful but superficial online access to existing services, or with the use of internet media for public communication, but also with deep, sustained investment in the kind of ubiquitous AI-assisted and AI-delegated operations that increasingly underlie most of the private economy. Politically, organizationally, and culturally as near-impossible as this might look.
The recently elected Argentinean government has made credible national statistics one of its earliest initiatives, less an act of futuristic boldness than a return to the 20th century baseline of data-driven decision-making, a departure of the previous government that was not without large political and practical costs. By failing to resort intensively to AI technologies in their public services, most governments in the world are failing to measure up to the technological baseline of the current century, an almost equally serious oversight.