Suppose backward time travel is possible. If so, it's probably of the variety where you can't change the past (i.e. Novikov self-consistent), because that's mathematically simpler than time travel which can modify the past. In almost all universes where people develop time travel, they'll counterfactualize themselves by deliberately or accidentally altering the past, i.e. they'll "cause" their universe-instance to not exist in the first place, because that universe would be inconsistent if it existed. Therefore in most universes that allow time travel and actually exist, almost all civilizations will fail to develop time travel, which might happen because those civilizations die out before they become sufficiently technologically advanced.

Perhaps this is the Great Filter. It would look like the Great Filter is nuclear war or disease or whatever, but actually time-consistency anthropics are "acausing" those things.

This assumes that either most civilizations would discover time travel before strong AI (in the absence of anthropic effects), or strong AI does not rapidly lead to a singleton. Otherwise, the resulting singleton would probably recognize that trying to modify the past is acausally risky, so the civilization would expand across space without counterfactualizing itself, so time-consistency couldn't be the Great Filter. They would probably also seek to colonize as much of the universe as they could, to prevent less cautious civilizations from trying time-travel and causing their entire universe to evaporate in a puff of inconsistency.

This also assumes that a large fraction of universes allow time travel. Otherwise, most life would just end up concentrated in those universes that don't allow time travel.