Yes. that's the worst spot. You could have an exhaust hood over the cooktop. This carries smoke, grease and fumes out of the house.

I can't think of one negative thing about staying cool while cooking. I agree that there should always be a vent-a-hood above range but that's a different issue to a discharge ac vent.

Well Klem1 there's a few wives tales about kitchens.

If you can't stand the heat, stay out of the kitchen.

Too many cooks, spoil the broth.

and baker's dozen is 13, not 12.

Easy bake and oven don't necessarily go well together.

Seriously though... typically you don't want a return vent to close to the kitchen, that's mostly about smells and grease being sucked back to your HVAC system.... a supply vent is a completely different thing. Other common fodder is putting in ceiling fans in a kitchen. This is mostly about cleanliness plus it just doesn't look good for long if you do a lot of cooking... grease spatter flung around by a fan? not a good idea.

If your home was recently constructed or the Kitchen recently remodeled, the supply may not be a conditioned air supply, but instead, a make-up air supply for the range vent hood. If it's a make-up air supply, it's most likely interlocked with the vent hood so that it only supplies air when the vent hood is operating.