No, they do not. Any car has brakes that can overcome its tires. All that is added by regenerative braking is the ability to lock the wheels more quickly.
Tires and weight (which EVs have a lot more of) are the larger factors in stopping distance.
Well yeah, that's why we have ABS right?
But there's more to it than that... having a good way to engine brake (and in this case regen) keeps your brakes cool and prevents them from overheating. Regardless of stopping power in ideal conditions, overheated brakes are not safe.
Brake discs on modern cars are vented and work like a centrifugal fan to cool them actively. They continually shed heat, so even dragging a brake pedal the entire way down a long mountain, as many drivers will do, is well within safety margins. So to overheat them, you have to get the heat in fast. Like 0-100-0-100-0-100-0 fast.
On the road, the only vehicles that experience brake fade are loaded trucks descending a grade, or suspects in a police pursuit.
A bit heavier, but not "a lot." A model 3 is between around 3600 and just over 4000 pounds, depending on trim. Not far off a similar size ICE vehicle.
To compare a car which is available in both ICE and EV, a 2018 Fiat 500e (electric, with a tiny battery bank good for only ~90 miles) weighs almost 3000 pounds, whereas the same car with ICE is ~2400lb.
25% more weight is a lot on a car.
That's all true, but I'm uncertain how much difference it can make. The bulk of the weight difference comes from the batteries, which will be there whether a retrofit or new design. Everything related to the ICE systems was removed, so it's not like there was any leftover weight from the conversion.
Weight distribution can likely be better in a chassis designed solely for EV, but total weight seems likely to be about the same either way.