There is the unsurprising twist that the Kree were the ones to kill "Lawson" in "Veers'" flashback, but that means that they know the McGuffin the Skrulls seek doesn't exist, that Carol destroyed it after they shot down her & Mar-vell's ship. Furthermore, the Kree also know that the energy source, which Mar-vell was keeping from them, was in "Veers" all along, which is why they brought her back to Hala and created a fake Kree identity for her. So, A. Why did they give a crap about hunting the Skrulls, since they knew the thing the Skrulls were supposedly seeking was gone, destroyed and all that remained, locked up in the body of one of their own people? Because the impression I got while the movie was going on was that the Skrulls were desperately trying to get this game changer tech, and the Kree were desperately trying to prevent them from getting their hands on it. But the Kree know it's gone and they have the only bit left over. Then there was the twist that the Skrulls weren't REALLY looking for it, just for their families, so why do the Kree give a shit?

Also, if she was what they were after all along, why was she not in a lab, or ANYWHERE but a front-line combat unit? Or if they wanted to use her energy as a weapon, what is the Watsonian reason for keeping it restrained with a chip and constantly trying to teach Carol self-mastery (the Doylist reason obviously being their allegory about people trying to suppress women)?