Correlation does not imply causation. Of course countries that are already involved in a joint-forces defensive military alliance are going to be more likely to

Correlation does not imply causation. Of course countries that are already involved in a joint-forces defensive military alliance are going to be more likely to enter into other external wars together. That doesn't mean the defensive alliance is somehow a contributing factor to that external war. Countries in an existing defensive alliance are likely using similar gear, have similar doctrine, have similar values, and have alignment strategic interests. The defensive alliance exists as an outcome of these alignments, as does the cooperation on the external war. The alliance doesn't cause the external war. Australia is not part of NATO, yet it's followed America into basically every war it's had in the last 60 years because of these preexisting alignments, not because of NATO.