There was an article about a parent who tried to do exactly that, in America. But the parent did not throw the kid into the deep end. For at least a year, the child was taken on those errands, being familiarized with the rule of the road, introduced to store clerks.

Ideas this author generated include — sending an older child along; secretly following to observe without intervening on anything less than catastrophic risks; sending the kid to neighbors to borrow a cup of sugar (and acquaint them to the neighborhood), and so forth.