Barbarians are planned as a threat to early eras. They should cause trouble, rob tiles and cities. Camps should require significant cleaning efforts. Perhaps the barbarians even need to be strong enough to be able to capture cities without walls by attacking them after turn 50, not just plundering them. In the early era, the barbarians really should be the main threat, and not a war with a neighboring great empire for the sake of a border town. Each civilization at this moment must ensure the safety of its territory so that the workers can begin to improve tiles, and not think about how to go and admire the beauties of a foreign capital.
By the way, I have never seen a barbarian horseman for 160 turns.
At the same time, it was possible to increase the number of barbarians at the moment of the foundation to 3 units, because Barbarians do not have combat advances, which give a bonus to CS, and experienced squads are destroying them without significant effort.