On further thought, I find that most of the serious 100% warmongers have the same problem. Attila just burns out faster than most. The issue is with the flavor system: the AIs like Shaka, Attila, and Genghis are all 100% war focused & have no plan "B" for when war stops working.
Attila has it the worst, as his units come very early, and he's not really good with the rams anyways.
For example, my most recent game with Shaka on my continent. It was myself (Montezuma), Harun Al-Rashid, and Shaka together for one little happy continent. I was at the North end, Arabia was a little South of center, and Shaka was at the very southern coast. Shaka utterly annihilated the Arabians, and started posturing towards me. I built up my force of upgraded Sword-Jags and bows, and actually declared war on him. There was some back & forth until I got Crossbows and Longsword-Jags, at which point I managed to wipe the floor with him. I resurrected Arabia and whipped the Zulus. Shaka offered me all cities but his southernmost one for peace, which I accepted... and then offloaded all the cities I didn't want onto my new best friend Harun.
Shaka had no plan B. I was snooping around his borders for the rest of the game, largely out of curiosity: all I ever saw was more freaking Impi, and him running a -50 gpt deficit. He never made it out of the Renaissance era, because he has no other setting but "build Impi".
I did discover that Longswords are absolutely the best thing to use against Shaka though - unlike the Musket that replaces them, Impi don't get the +25% bonus versus "gunpowder" units and remain outmatched. If your Longswords are highly promoted & have Jaguar abilities, the Impi swarms barely stand a chance.