There are some really good books about wars between cultures that have AGI and it always comes down to math - whoever can get their hands on more compute faster wins.
This is also a strong argument for immigration, particularly high-skill immigration. In the absence of synthetic AGI whoever imports the most human AGI wins.
Which suggests that total AGI compute doesn't matter that much, as India isn't the world leader the amount of human compute they posses would suggest then.
What matters is how you use the AGI, not how much you have, with wrong or bad or limiting regulations it will not lead anywhere.