And goody huts/tribal villages too ! Otherwise I don't like too much the term "minor factions", at least clearly depicted in a gameplay mechanism.
"Minor Factions" is so generic as to be near-meaningless. It could describe anything from the current Tribal Huts to City States to a playable Civ trying to go Tall when everyone else on the map is going Wide.
On the other hand, I think the game is well-served by having several different Less-Than-Playable-Civilization type entities on the map. The current heirarchy from least to greatest is:
Tribal Huts - ephemeral, disappear as soon as contacted.
Barbarian Camps - one-dimensional, and have always seemed to be included to provide some kind of opposition when the AI doesn't
City States - a good place to park potential Civs that cannot be modeled as playable, either because their language and leaders are Unknown or they were too historically momentary or non-city-building to provide a city list. Given that they could be programmed to spawn units as fast as Raging Barbarians do now, this category could actually be much more useful than it is now: they could represent everything from Scythians to Saami, large tribal groups, semi-nomadic groups, and a host of others.
Playable Civilizations. - which, because the City States are rather under-utilized, includes some dubious contenders, especially among the modded Civs which can get away without languages, well-attested City Lists, or leader portrayals.
I have argued for some time that the best change to this system would be combining the Tribal Huts and Barbarian Camps into one category: Settlements, which could be either friendly or hostile or neutral, trade information, resources, provide units or provide a continuous raiding nuisance - the Barbarian Clans Mode, but with additional features from the Tribal Huts so that these are not necessarily Always Hostile and to be eliminated ASAP.
I would particularly like to see Settlements and City States be sources for Resources not otherwise easily available or special units as Mercenaries to be hired: Horse Archers, specialized Slingers spring to mind, or the historical trade in Amber, metals and other materials frequently done in the Classical era by Non-State actors.
Given that on average a game has twice or more as many City States as Civs in it, and at least 1 - 2 Camps/Huts for each Civ or City State, this would open up a much wider range of interactions throughout the game, economically, militarily, diplomatically, and even with regard to culture/religion.
And finally, this re-design of the Barbarian/Tribal characters would allow us to more accurately model the interactions of new Colonies with their neighbors instead of having those interactions defined by the type of neighbor and independent of the colonizing gamer's actions.