If the AI has a naive "save humans" utility function, I don't see how this advantages it.

I've met people who can lucidly argue that nuking a particular city or small region would produce many benefits for humanity as a whole, including reduced risk of politically-motivated extinction events down the line.

Also... you're going to an awful lot of trouble, here, to calculate a firing solution for a beam of light to hit a non-accelerating object in space. Realistically, if we know where the comet is well enough to realize it's headed for Earth, aiming a laser at it with non-sapient hardware is almost trivial. Why not an NP-complete problem?