The main function of this type of training is to eliminate the ball as a variable in the decision making process. At the professional level, when the ball is passed towards a player, they don't need to think about how they will control it, which foot they will use, how to counteract the spin on the ball... all of those details are processed instantly because of all the time they have spent with a ball their entire lives. This is backed up in part by a study examining Neymar's brain activity while moving his foot versus other soccer players, athletes, and regular population. This frees up players to focus on the positioning of the opposition, their teammates, where the goal is, etc. We have all seen a young player receive the ball under pressure, and turn right into a defender. We all know the player made a poor decision, but more often that not, it is because they had to focus so much attention on controlling the ball, that they were unable to perceive the defender closing them down.
For younger players, up until maybe ages 12-14 (depending on the level), it is my opinion that most of their time outside of team training should be spent on 'volume training', involving the activities above. Just the player and a ball should be enough most of the time, along with some form of pickup or other informal play peppered in.
For the very youngest players (1-6), Tom Byer has more understanding than anyone else I have come across. This article presents his views very well. His advice is simple: always have some small balls (all the way down to the mini size 1 balls) around the house, and teach them the sport is not a kicking game. Encourage them to dribble, stop, and turn with all parts of their foot, and with both feet. These are things even parents who did not grow up playing the game can do. As they grow in skill and confidence, they will be more likely to play and train on their own.
For older players, identify an area inside or outside the house as their designated training area. Show them some of the above videos, provide them with a ball and maybe a couple cones, and replicate them exactly the first couple times. Once they get the hang of them, encourage them to find a way to increase the difficulty, or complete the footwork at a faster speed than the day before. Encourage them to time themselves, or reach a set number of touches, so they can measure their progress. Find a spot at the house, or at a local park or school, where they can kick against a wall. You can also build one out of plywood, or invest in a rebounding net.
It also helps to have a set schedule. Maybe their individual training time is in between World Cup games, or before lunch, or when they get back from school or daycare, or for 15 minutes before they leave for school. Maybe they will ask you to drop them off early at training, or stay late, so they can work on their individual skills.
Keep a soccer ball or two in the car, so if there is some downtime somewhere, they can pull it out and juggle, or pass with a sibling, or play 1v1 with whoever else is around. Make the ball an ever-present wherever you travel. It will be a good way for them to blow off some steam on car trips, and get away from any handheld electronics. If they can, they should keep a ball in their backpacks or lockers, even if it is just a size 1 or 2 mini ball.
Encourage the players to set up their own regular games at your house, a friend's house, or down the street. For example, every Wednesday at 4 pm, Jacob and Jimmy and Johnny will all meet me at the park and we play until 5 pm.
All of these different activities are part of a virtuous cycle: as they get better and improve, they will enjoy playing more. If they enjoy playing more, they will do it more often. If they do it more often, they will get better... This carries over to team training as well. Players will go to and leave training in a better mood, more excited to play, and more motivated.
The dirty little secret about player development is that so much of it happens at home, away from a coach, and away from organized play. Somebody like Messi or Neymar or Hazard didn't develop to a world class level because they played for the local academy 3 times a week for 90 minutes when they were 10 years old. Coaching absolutely plays a role in developing these players, but it is simply the tip of the iceberg.