Desktop gaming GPU's consume 250 watts + of power, a laptop wont be able to power a GPU, Wont be able to cool a GPU, would have to be massive to fit one inside, and the power brick would have to be gigantic. At this point just get a mini ITX build it would be cheaper and more functional.
1. Noise - Laptops would make a lot of noise if it had a desktop graphics card
2. Size - The size available in most laptops are too small to fit a desktop graphics card
3. Heat - Most laptops would overheat as the Gpu requires a lot of cooling
4. Battery life - It will greatly shorten battery life.