I think it's much more likely that the AI turns out not to be as compliant as the capital owners expect, and they die too.

However, that's not useful in predicting what capital owners will do, because they follow their local incentives. "If everyone keeps doing X, we will all be worse off" does not help unless you can create local incentives that point toward an equilibrium where everyone stops doing X.

In this case, no capital owner is individually better off by unilaterally refusing to chase more efficient returns on their capital. We would need an international agreement, with enforcement mechanisms, like I mentioned above.