I really don't think that military alliances increase the likelihood of conflict because within a military alliance network, you don't attack the ally of one of your allies. The number of international wars has dramatically decreased in the last 70 years.

My guess would be that China likely hasn't attacked Taiwan, Korea, Japan, etc because they have strong military allies, not because its trading a lot with them.

I don't truly believe that NATO was the reason Putin invaded Ukraine.
If that was the reason, it has backfired spectacularly, now that Finland and Sweden have joined and Putin has lost half his army. He can stop killing Ukrainians and stop sending Russians to die at any moment... but he's unlikely to, I think. I really don't understand how he can claim any sort of victory at this point.

We might not ever know exactly why Putin decided to invade Russia, I think it was either to reestablish the Soviet Union or to grab Ukraine's resources like natural gas and lithium. Without ally support, many more Ukrainians, particularly non-combatants, would have been murdered by Russian soldiers.