Laptops can also be used for gaming. High end gaming laptops have gpu as powerful as a gtx660. Though the ones that has great hardware in it are usually expensive as one would expect already
Maybe, but they run hot, are more prone to breaking and be almost double the price with a comparable gpu. Not to mention they're hardly serviceable/repairable at all.
As far as value goes, a good desktop gaming PC will cost about 250-400 dollars a year but a laptop would be like 600-800 dollars a year of life.