It'll get a lot of time to react at that energy as it's not going to "instantly" fry anything*. That's probably less energy/m2 than consumer heat guns, especially if consider that these drones are likely going to get sprayed in reflective paint. Easy defense for the drone would be just: get into a spin to get roasted evenly -> shut off -> fall for a few hundred meters, cooling using air that rushes by to counteract the laser further -> catch itself once it lost the laser.

That would force these laser systems to point each drone until it either visibly goes up in flames or impacts the ground (which means you also need to be able to track them all the way down), otherwise you can't be sure it won't just snap back to life once you started engaging the next drone.

I don't feel like 10kw/m2 would be anywhere near useful. It's gotta be more than that.

* Stadium floodlights aren't going to instantly grill any bird that flies in front of them either, and they reach that ballpark.