Suppose we have an electronic equipment (say a TV) that is rated 200W, 1A, 220V. If the voltage is reduced say to 100V (or even less), why don't the TV run drawing 2A current as the power is again 2x100=200W.
Is it because of the protection devices that don't allow or there is some other reason?
You assumption isn't necessarily true. Some electronic devices have a wide range supply, e.g. 100 - 240 V nominal range. The behave exactly as discussed, maintaining a constant power. A single range device is required to work at -10% or -15% of nominal mains voltage, but not below.
Generally, only devices with a SMPS (switch mode power supply) can have a wide range input (but they don't necessarily have), transformer supplies can't.