Disclaimer: I know these are game design decisions.
When saying “series” I’m counting at least two games.
Polearms, especially pike
They are not trash units good against only cavalry. Polearms have been the bulk of the army and the most effective melee weapons in general for most of the time.
And the polearm names are rarely correct. In AOE2 “pikeman” uses something like a voulge or guisarme. In AOE4 “spearman” carries almost every single type of polearm that existed.
In AOE3 pikemen thankfully use pikes but they are still trash units.
Arquebus
In AOE2/4 arquebuses were too late for the period so they only appear in a few civs as “better handguns”. In fact they quickly replaced handguns and dominated the battlefield in 15th century.
In AOE3 however to contrast the “heavy” line infantry (musketeers), earlier arquebusiers who assumed more of a skirmishing role were assigned to the same role as rifle-wielding skirmishers (longer range, bonus against heavy infantry).
A more accurate role would be a generic gunpowder unit, and musketeers and riflemen are more specialized branches of upgrade.
Projectile weapons
Slings/Javelins always assuming a “counter ranged” role is very incomprehensible to me. I guess it is because the bow/crossbow/musket usually fulfills the role of generic ranged weapons, and others are usually thrown into remaining roles, most of the time a counter unit.
I cannot think of more appropriate roles that do not overlap with other ranged units however, because there weren’t a lot of “real” counters in reality either. Maybe slings have greater generic damage and javelins have a armour-piercing ability.
Another difficulty is that (similar to AOE3 arquebuses), in reality skirmishing units do not necessarily have longer range, but in the game you usually have to make them do.