Mine want to run barefoot
Mine want to run barefoot with me. I let the oldest. He stays mostly on the grass but will jump onto the asphalt from time-to-time. They like playing outdoors with their shoes off. They just run right on out the door.
About kids running on grass (other than the fact that there are hidden dangers in grass), I don't think they have to stick to the same practices we older adults do when it comes to practicing "proper" running form on harder surfaces first. I've witnessed my children running plenty, and no matter what surface they are on, they have proper form. I think it's more inherent when we are new to life, and we lose it as we age and get away from that youthfulness of just being free.