If you cook, yes. Definitely.

Not just for the smoke if something were to burn, or the humidity control when a liquid is boiling, or the heat it puts out that your AC will have to fight off, but also for the oils and odors that will, after time impregnate themselves into your walls, ceiling and cabinets.

There is more than one way to skin the cat.
[houzz=]

Need? no. Do you ever burn food? If so possibly yes. Smoke can discolor paint in a hurry. It is an expense but could be cheaper than repainting an 11 foot tall ceiling not to mention lingering odors.

They are not my first choice, but I think we're hearing some kickback to an overhead and want to point out an option other than 'no'....I defer, though: 'do it, or repaint' is a stronger argument than 'vent weakly, rather than have none".

If you don't cook, that's another story, but even steaming vegetables aerosolizes vegetable oils to float around an open concept with no direct kitchen ventilation. Not to mention the heat, steam, grease, and smoke that will stay in your home, coming into contact with your new cabinets and furniture, and depositing on them.