Agreed. It's an interesting question whether we want governments to realize it or not. I lean toward the "yes" side (in general, it seems better when governments understand catastrophic risks), but we should debate the question more before taking action.
Summary
I think there's a decent chance that governments will be the first to build artificial general intelligence (AI). International hostility, especially an AI arms race, could exacerbate risk-taking, hostile motivations, and errors of judgment when creating AI. If so, then international cooperation could be an important factor to consider when evaluating the flow-through effects of charities. That said, we may not want to popularize the arms-race consideration too openly lest we accelerate the race.
Will governments build AI first?
AI poses a national-security threat, and unless the militaries of powerful countries are very naive, it seems to me unlikely they'd allow AI research to proceed in private indefinitely. At some point the US military would confiscate the project from Google or Goldman Sachs, if the US military isn't already ahead of them in secret by that point. (DARPA already funds a lot of public AI research.)
There are some scenarios in which private AI research wouldn't be nationalized:
It seems that both of these bad scenarios would be exacerbated by international conflict. Greater hostility means countries are more inclined to use AI as a weapon. Indeed, whoever builds the first AI can take over the world, which makes building AI the ultimate arms race. A USA-China race is one reasonable possibility.
Arms races encourage risk-taking -- being willing to skimp on safety measures to improve your odds of winning ("Racing to the Precipice"). In addition, the weaponization of AI could lead to worse expected outcomes in general. CEV seems to have less hope of success in a Cold War scenario. ("What? You want to include the evil Chinese in your CEV??") (ETA: With a pure CEV, presumably it would eventually count Chinese values even if it started with just Americans, because people would become more enlightened during the process. However, when we imagine more crude democratic decision outcomes, this becomes less likely.)
Ways to avoid an arms race
Averting an AI arms race seems to be an important topic for research. It could be partly informed by the Cold War and other nuclear arms races, as well as by other efforts at nonproliferation of chemical and biological weapons.
Apart from more robust arms control, other factors might help:
Are these efforts cost-effective?
World peace is hardly a goal unique to effective altruists (EAs), so we shouldn't necessarily expect low-hanging fruit. On the other hand, projects like nuclear nonproliferation seem relatively underfunded even compared with anti-poverty charities.
I suspect more direct MIRI-type research has higher expected value, but among EAs who don't want to fund MIRI specifically, encouraging donations toward international cooperation could be valuable, since it's certainly a more mainstream cause. I wonder if GiveWell would consider studying global cooperation specifically beyond its indirect relationship with catastrophic risks.
Should we publicize AI arms races?
When I mentioned this topic to a friend, he pointed out that we might not want the idea of AI arms races too widely known, because then governments might take the concern more seriously and therefore start the race earlier -- giving us less time to prepare and less time to work on FAI in the meanwhile. From David Chalmers, "The Singularity: A Philosophical Analysis" (footnote 14):
When I discussed these issues with cadets and staff at the West Point Military Academy, the question arose as to whether the US military or other branches of the government might attempt to prevent the creation of AI or AI+, due to the risks of an intelligence explosion. The consensus was that they would not, as such prevention would only increase the chances that AI or AI+ would first be created by a foreign power. One might even expect an AI arms race at some point, once the potential consequences of an intelligence explosion are registered. According to this reasoning, although AI+ would have risks from the standpoint of the US government, the risks of Chinese AI+ (say) would be far greater.