No a high speed missile cannot change its course willy nilly. It will experience massive G forces. Russians already had a solution keep the missile frame rotating so the heat is dissipated. Same reason why the Shaurya missile also rotates in flight. Laser system is very useful against aircrafts and sub-sonic cruise missiles. They cannot keep spinning. Laser and EMP systems are required for the future and will be in service in a decade or two. The time to do research on them is now not then.