Yeah, you'd think they would try the lasers, too, if they were that desperate. But you'd also think the Axanar ship would be able to guess that the ship that won't respond to his hail, and is attacking the other ship, is the villain.
For that matter, is this likely to be a "new" thing? Wouldn't there be a history and the Axanar would already know if there's someone out their who thinks of them as a resource to be harvested? But this is television. They have to crank out stories very quickly and deliver their 22 episodes per season.