I don't think greed or spinelessness have anything to do with it. AI is similar to nuclear weapons : Any country that doesn't have military AI will have a huge disadvantage against a country that does. Every country rationally believes that AI will improve their military chances, and every country rationally believes that every other country desires AI for their military as well.
China and Russia will certainly build AI drones as soon as they possibly can. The only thing that happens if western countries don't build them is that they are at a significant disadvantage.
This is also true of chemical and biological weapons, and weaponizing outer space, but countries have managed pretty well at not going into an arms race in those areas; even nuclear weapons have been reasonably well kept in check. But these mutual agreements to not pursue certain lines of military technology (at least for offensive purposes) really need to start from the strongest military agreeing to not do it and allow monitoring/audits to get other countries on board. The US doesn't seem all that interested in that with AI, or other scary technologies on the horizon. (Without even getting into the issue that AI is trickier than something like a chemical weapon, countries would have a field day on what actually constitutes AI vs normal digital automation...)
> This is also true of chemical and biological weapons
I disagree actually. Nuclear weapons render chemical and biological weapons moot, and no major superpower is willing to give up nukes. The United States has no need for chemical and biological weapons because it's keeping it's nukes. I think that AI will present a comparable advantage.
Also, AI does not (yet) create the sense of dread in the popular imagination that nukes did during the cold war. Incinerating an entire city in a few seconds is terrifying on an existential level to any human. Having computers control drones and tanks seems.. almost boringly inevitable, by comparison. I doubt there will be unified political will to prevent it.
Also, I think the international climate has radically changed. Agreements like TPP, which the powers that be supported, were not able to pass. In the era of Trump I highly doubt there is enough global trust for Russia or China to agree not to research militarized AI. Basically I don't see a single major power agreeing not to develop militarized AI in the near future.
China and Russia will certainly build AI drones as soon as they possibly can. The only thing that happens if western countries don't build them is that they are at a significant disadvantage.