If the AI keeps on recruiting units close to its maximum capacity, it will be forced to produce fairly balanced historically plausible armies thanks to M2TW system of recruitment pools and replenishment rates, which we are using very thoughtfully to get as much from it as we can.

Therefore if the AI decides that it likes slingers and slingers only, such slinger stack would be very far from endless because it will only be possible to recruit only one unit per a given amount of turns.