I don't think they knew they would become the next Levelers. Only Myth 3 says that Connacht knew the future. But not everyone sees Myth 3 as canon to Myth.
Even if somehow they knew, maybe they all thought the Leveler was gone. I mean when Tireces defeated the first Leveler, no one likely knew there was a cycle. When Moagim first appeared, most probably didn't even know he used to be Tireces.
So by the time Connacht was around, they didn't have enough information on the cycle. They might have thought it was just some other bad guy. Maybe even a one time thing that a great hero would return as a great destroyer. Even during TFL/M2 it sounded like most people do not know about the cycle or do not believe in it.
Maybe Alric thinks he broke the cycle for good, so he won't just end his life.