DHAKA, Bangladesh—This sprawling city of 14 million, growing fast, suffers the developing world's best-known ills: crushing poverty, tangled traffic and overburdened services that leave piles of pungent waste scattered across the city.

But the government's latest plan to bring Dhaka under control by splitting the city into two parts, each with its own bosses, is only making matters worse, many residents say.

The...