If you are wondering about building codes, then no you don't "have to have a vent hood". But if you are asking about indoor air quality, cooking smells, and grease on your cabinets, then yes, you probably should have a hood. I clean the baffles on our hood every couple of weeks, and there is quite a bit of grease that I remove each time. The good news is, with a well-built hood, cleaning is as easy as putting the baffles into the dishwasher. The bad news for you is that all this grease would get spread all over your kitchen, if you don't have a hood. So, I absolutely would recommend one. I don't think they look ugly at all. But as always, that really depends on how good your kitchen designer or architect is: Noise on the outside of the house is negligible. I can stand three feet away from the vent opening, and I can't hear more than a bit of a whispering rush of air. Noise on the inside when the hood is in use is a different thing. You'll never be able to completely eliminate that. If it does it's job, it needs to move air. And that makes noise. But if you have the space, you can install a remote blower and in in-line silencer, and that will cut down on a lot of the noise. Of course, that also costs more money. Speaking of money, you are likely to also need a make-up-air system. That can get expensive, depending on your climate. In a moderate climate, it might be as simple as another motorized damper in your heating system. But in other parts of the country, you might need a heated make-up-air system, and those are pricey. The good news is that with induction, you can often get away with slower flow rates for your hood. So, whereas we have a 1200 CFM hood, you quite likely wouldn't need anything quite that powerful. That'll make it cheaper and less noisy. As a general rule though, do the math on the CFM that you need (see other postings on Houzz; look for anything by @kaseki), buy a hood with baffles rather than mesh filters, and have at least 3" extra overhang at both sides. If possible, have as much overhang in the front as you can do. Also, tell your contractor to put really big ducts in; that'll reduce noise and allow the hood to work much better. 8" or 10" diameter is really what you should have. 6" won't work well at all. All of those things will make the hood more efficient and easier to use. Build a cardboard mock-up first, and use that to determine where you want to mount the hood. We mounted it above head height, and that's really nice, as it doesn't get into your sightlines. But some people prefer to mount their hoods lower.

I hired a local HVAC company to redo mine. They didn't change the location, my dryer is vented into the floor, under my laundry room and vented outside ground level near my patio in back. It was a spliced together 'mess' of more than one material and some of it original to the 1955 house. Replaced with a straight shot of stainless - worth every penny I paid ;0)

That's some improvement and you had a short run to outdoors to start with. Probably will see a bit more with 'normal' mixed loads. Looks much cleaner & will be lots easier to clean. I replaced about 4' of semi-rigid flex with solid, changed the louvered vent outside with a ball seal (Lambro Vent Seal) and got the vent actually connected to the outside vent opening. DH had installed it originally; the tubing was not even connected to the tailpiece of the exhaust on the outside of the house! And no tape. Was a bit of a nightmare getting it connected because it exists thru the rim joist. So I had to work back in the recess over the foundation with floor joists over my head. Got it connected & taped up now. The space was so limited that I had to use 4-6" long pieces of tape to seal the joint. Combination of about everything that could be wrong was wrong. The periscope gained me about 2" of floor space, too. Which was huge given how tiny the laundry area is. Looks much more tidy and the reward was a big reduction in dry times.

It is not possible to go through roof since the bathroom is in the basement. The dryer vent was put in when the house was built new 5 years ago and passed inspection then. The vent runs underneath the floor joists and is the shortest route to the outside. The dryer vent has 3 bends in 20'. It is working fine with no issues whatsoever. I was planning to use insulated flex for the bathroom vent since I heard it was best for it to be insulated.