idk about vertigo specifically (and things laypeople diagnose as vertigo), but yes in that I had a family member who was exactly in this situation. Walking sticks and still very concerned with falling while getting to a cart, then perfectly stable after being able to grab onto something in front of them. Though I highly doubt they themselves left carts around the lot rather than returning them to the closest corral.
If someone has vertigo that does not allow them to push a cart for few meters, then maybe this same vertigo means they shouldnt drive a car at all.
Because they can cause an accident and kill themselves, or others.