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.

Remember HOGS:

Heat
Odors
Grease
Smoke

You need a quality venthood to keep the HOGS out of your kitchen.

Important when dealing with an island is to find a hood that covers enough space so that the HOGS can’t escape when rising.

Don’t bother with those small island vents that sucks from the back of the stove, you may as well have nothing at all.

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.

We lived in condos and townhomes for years, had the cheap over the stove hoods with microwave on top... smoke detectors always going off. Now we have an open floor plan house that has flat electric cooktop on island with down suction vent. No smoke alarms going off but anything good cooking, you’ll be smelling for a day or two in multiple rooms. Wish I had the money to convert to gas with hood but we probably won’t be here long so f it. We tried to get seller to replace cooktop because it has multiple cracks but they said no

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My house doesn't have one. I wish I did sometimes

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This is me. It doesn't stop me from cooking anything, but some dishes will permeate through the house and linger for a day or so. I think a vent would help that.

ETA: We had a downvent behind the old stovetop before we changed out the granite and I opted to not reinstall because it was completely useless. Have been considering putting a hood in recently, just haven't pulled the trigger.

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We lived in condos and townhomes for years, had the cheap over the stove hoods with microwave on top

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The worst part about these, is that they are recirculating hoods. The smoke is not being moved out of your house, instead, it just goes through the filter and the "clean" air blows out the top of the microwave.

Not very effective.