Lasers can stop a hypersonic missile, but the challenge is getting a beam on the target through the atmosphere. Some of the old SDI tests solved the problem by flying the laser above most of the atmosphere.
First, asymmetric ablation can destroy hypersonic vehicles extremely quickly. It is a major cause of failure in hypersonic vehicles even when no one is shooting lasers at it. A laser just needs to induce the ablation asymmetry; the physics of hypersonic vehicles will do the rest of the work.
Second, precision terminal guidance systems can't function behind ablative shielding. The terminal guidance system has no protection from high-power lasers.
The current lasers are not powerful enough for this purpose, they may be efficient only against drones or other slower targets.