Another limitation of archery units past their historical eras is that in the 1upt system, there's only so much space to deploy units, and with a 2-hex bombardment range, things may get a little tight when trying to move ranged units into a position to fire on a given hex. Archery units have to compete with siege units for this space, and once they start competing with Cannon, that's a much easier choice.
There really is no Renaissance equivalent of archery units. Grenadiers were for assaulting fortifications (during the brief historical period in which Grenadiers actually used grenades; after that they became just an elite infantry unit); you can't really even throw a grenade the 20-50 range of a musket, much less over the friendly unit in front of you.
In the modern era, I don't think there's really any need for such a class of units, with longer artillery range and close air support.