Just last month here in north Texas we had a four year old lose his entire leg due to a lawn mower. Grandpa was mowing and he was running around in the yard playing. Apparently grandpa made a sharp left turn and he was there and was pulled under the deck.
I understand having the kid on the mower isn't the safest thing but at least you know exactly where they are. Personally I think if you don't have someone to watch the kids your lawn can wait to be mower. Safety ahead of aesthetics or vanity. Just my opinion.