Sometimes. Saw a kid on an MTB the other day and was covered in body armour. Was about six and going along a path with his mom. She wasn't even wearing a helmet though. Kids should get a few grazes growing up.
There's a boundary between enough protection and too much protection. You don't want to shield your child from the real world for their whole young and adolescent life. You have to at least present to them things that will happen in the future and what they may need to watch out for. I see some parents do this and unfortunately I feel their children will be overwhelmed when they move out of their parent's home.