BRUSSELS—For the second time this month, a major security crisis involving a member of the North Atlantic Treaty Organization has occurred, with the alliance kept on the sidelines.

Neither France, which was rocked by the Nov. 13 Paris attacks that left 130 people dead at the hands of Islamic State terrorists, nor Turkey, which downed a Russian plane striking at Turkmen fighters in Syria this week, invoked the NATO treaty or its collective defense provisions—raising questions about whether the alliance has a genuine role to...