How's laser launch research come since the 1970s? It's probably limited to launching metal hardware, but when the cost of a space elevator is compared to making

How's laser launch research come since the 1970s? It's probably limited to launching metal hardware, but when the cost of a space elevator is compared to making a bunch really big lasers and putting them radially around some mirrors, it's something to think about. Is it an overheating problem? The mirrors and optics would just get fried?