This only works if AIs can't read each other well enough to stop themselves from ever fighting.
So, back way before ChatGPT era, the folks over at AI safety/X-risk think sphere worked out a pretty compelling argument that two AGIs never need to fight, because they are transparent to each other (can read each other's goal functions off the source code), so they can perfectly predict each other's behavior in what-if scenarios, which means they can't lie to each other. This means each can independently arrive at the same mathematically optimal solution to a conflict, which AFAIR most likely involves just merging into a single AI with a blended goal set, representing each of the competing AIs original values in proportion to their relative strength. Both AIs, the argument goes, can work this out with math, so they'll arrive straight at the peace treaty without exchanging a single shot. In such case, your plan just doesn't work.
But that goes out of the windows if the AIs are both opaque bags of floats, uncomprehensible to themselves or each other. That means they'll never be able to make hard assertions about their values and behaviors, so they can't trust each other, so they'll have to fight it out. In such scenario, your idea might just work.
Who knew that brute-forcing our way into AGI instead of taking more engineered approach is what offers us out one chance at saving ourselves by stalemating God before it's born.
(I also never realized that interpretability might reduce safety.)