Is it better to let children play as they wish, or to restrict them, and what are the most prominent Prophetic hadiths concerning this matter?

It is better for boys to be given space to practice various types of games and sports, provided that no harm or شرعي (religiously forbidden) act results from it, and they should be supervised so that it remains within the bounds of their benefit and does not conflict with their other interests. Useful games such as swimming, archery, and horsemanship should be chosen, for in the Hadith: "You must shoot arrows, for it is of your best pastimes," and "Everything that is not the remembrance of Allah, the Exalted and Glorious, is amusement, except for four things: a man's walking between two targets, his training his horse, his playing with his family, and teaching swimming," and "Teach your boys how to swim."