I've only played a few factions in EB1 (Aedui, Epiros, Getai, Pontus) but it seemed that those factions purposefully started with more units than they could afford to maintain, forcing the player to either (1) disband some of their units or (2) immediately capture a nearby city.
Keep in mind that the A.I. gets money already, and even bigger bonuses depending on the difficulty. Factions played by a human will generally always be losing money, this isn't the case for the A.I. playing the same faction.

I would actually like to see a better system than just unlimited money for the A.I. That is why I mentioned the script done by Fred Putz a few posts up. I feel it has more depth than just unlimited money, and is said to offer a variety of benefits; for example, the ability to wage economic warfare. You should check out some of the links above, they have greater detail.