Well, in the short term at least, killing off all the Air Nomads meant Sozin would have a break of twenty years or so waiting for the next one to be born and trained -- and he was old enough at that point that it might have been a matter of conveniently leaving the problem for the next generation. ;)
But then when the Air Nomads were all gone and no new Avatar showed up for a hundred years, well, maybe they figured the cycle was already broken somehow. (And that may be the case anyway when Aang eventually dies, unless there's a secret hidden population of surviving Air Nomads somewhere -- three more rounds of reincarnation after this one and whoops, dead end, no more Avatar cycle!)
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timeasmymeasure
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But then when the Air Nomads were all gone and no new Avatar showed up for a hundred years, well, maybe they figured the cycle was already broken somehow. (And that may be the case anyway when Aang eventually dies, unless there's a secret hidden population of surviving Air Nomads somewhere -- three more rounds of reincarnation after this one and whoops, dead end, no more Avatar cycle!)