I would have said 'The cook always cooks tasty food' is not the same as 'The cook is always cooking tasty food' but I'm not sure if the Swedish sentence can be translated both ways.
Why does "the cook always cooks good" not work here? Is it because of the "mat" at the end rather than directly behind "lagar"?
It's because how English works. If you don't have an object, you'd say The cook always cooks well. If you include the object, you can say The cook always cooks good food.