I'm not sure why you would want to control for this. Creating these kind of political and cultural blocks is one of the mechanisms by which democracies act and influence the world.

Is there evidence that the democracy caused the creation of the blocks? To me it looks more like the blocks were there to begin with - for political and historical reasons - and because dominant members of the blocks were democratic and some of them strongly pushed for democracy in their foreign policy, democracy spread and lasted inside the blocks.

E.g., Western and Southern Europe has been almost entirely democratic post WW2 because the victors led by the US demanded it. If the Nazis had won, or if the USSR had conquered Western Europe, then they would not have been democratic. That's another (and obvious) sense in which it's a historical coincidence, not predictable beforehand, that Western Europe is democratic.

It's true that the block(s) define themselves, today, as democratic and won't allow tight integeration with non-democratic countries. But what countries are there whose regimes actually changed as a result of this policy? Probably a few and a few more where it was a factor, but AFAIK nothing much on a global scale.

To me that suggests that democracies preserve political capital by redirecting their wars against the outsiders, while not forgoing wars at all.

Doesn't this support the original statement, which was that it's not a coincidence that "the most powerful military and economic global alliances consist mostly of democratic countries"?

It's a method by which such alliances maintain their power, but it's hardly powerful enough to be the main reason they became paramount in the first place.

If during WW2 (and plausibly also during WW1), the US had been anti-democratic - then the post-war world would almost certainly not have contained any democratic countries in Europe. If we count countries and not people (which is reasonable when discussing alliances and power blocks), then a regime change in just one country would have (with significant probability) reversed the regime outcome for the whole world.