As jrockway mentions, the ATMega does not have a power regulator. That would be inefficient as regulators work by dissipating excess energy as heat. So, even if the chip had onboard regulators to limit the combined current draw of the output ports to 200mA the chip would still be susceptible to overheating.

That said, I'd guess the weak link that puts the 200mA limit in place is not actually in the I/O circuitry but is how much current can safely be drawn by the I/O pins when the chip is otherwise fully utilized - peripherals and CPU both consuming max power.