Are hood vents necessary over island with electric cook top?

I would only if for a means to evacuate the heat/steam higher into the room.

I can't think of an actual need though.

I personally think range hoods that vent outside the building's envelope are ALWAYS a good idea, just from an air quality standpoint, even if they're not strictly necessary. Getting smoke and fumes out of the building is a nice thing to be able to do. You just have to make sure they're kept clean so they don't become a greasy fire hazard and you have to make sure they're properly sized
by an HVAC professional not only to make sure that there is enough flow to properly vent the space, but also that the vent is properly matched to the house's ability to let air in to replace the air the vent tosses out. The vent needs to be sized to make the kitchen just a little bit lower in pressure than the surrounding rooms so fresh air flows into the kitchen to replace the air being vented instead of smelly kitchen air being able to get out into the surrounding rooms. Too little capacity is a bit of a waste of money because smoke, fumes, and moist air will just fill up the hood and escape into the kitchen and then the surrounding rooms. Too much capacity or the right amount of capacity but insufficient fresh air supply to make up for the air being vented, though, can cause some severe negative pressure problems.

I've seen a grossly oversized range hood in a commercial space once that pulled so much negative pressure that the double swinging doors from the kitchen to the dining rooms would stay open with about 4 inch cracks between the doors from air rushing into the kitchen and there was some moisture intrusion from air getting sucked into the kitchen hard enough through normal cracks in the building envelope to drag water in with it on a rainy day.

Of course, if the hood just vents back into the room to move air from the stove area to elsewhere in the kitchen, the negative pressure problems cannot exist, but you're also not getting rid of the "contaminated" air. It's still better to disperse that air instead of letting it just hang at the cooking area. Also, check and see what your local building code has to say, just in case there's something in there about range hoods.

It really depends on what you cook and how you cook. I wouldn’t live without a good hood. Mine is commercial, but I have gas that includes an indoor gas grill.

I don’t have one, but sort of wish that I did. Planned on it but have just never installed it.

I just don’t cook heavy grease (ie frying) inside. I don’t even seer steaks inside because I can’t get the grease out the air.

I have gas. But no, they aren’t necessary, but you may have to alter the way you cook.

Yes, if you actually cook. Imagine making a stir fry without one....every upper surface in your kitchen will end up coated in oily residue. Or onion rings, or seared tuna.

Lots of pretty kitchens don’t have them, or have inferior, low flow ones. So many ppl today just don’t cook.