It may help to realize, they don't do that simultaneously. 200A * 1000V is a lot of continuous power, but they are operated under those conditions for a fraction of a microsecond at a time. The rest of the time, they are dropping 200A * 2V or so (whatever Vce(sat) is at that current, and temperature), or 1000V and <1mA (whatever C-E leakage current is).
Indeed, they are designed exclusively to do this! The amount of power an IGBT can dissipate, while at high voltage, is severely reduced compared to other types. IGBTs are not recommended for linear operation, such as in linear regulators, power amplifiers, etc. They are only good for switching, and they are damned good at it, too!
Tim