The first question is what gap you are actually trying to close. Extra training only makes sense when you know what you are training for.
At 11-12, the most common gaps: weak foot, first touch under pressure, finishing, and speed of decision-making. All four are real and all four can be worked on outside of team practice.
None of them require expensive sessions. Most of them require a ball, a wall, and 20 minutes a day.
Individual ball work at home: this is the most effective thing a developing soccer player can do. Juggling is the most basic version, and it builds touch, coordination, and ball familiarity in a way that team training cannot replicate because team training never gives an individual player enough repetitions.
Ten minutes of juggling and wall passing per day, done consistently over a year, produces a measurably better player. The catch is the word consistently.
Private training sessions: worth the investment when the training is targeted at a specific weakness and the trainer is actually observing and correcting. Not worth the investment when it is generic “individual training” that covers the same ground as team practice.
Ask a potential private trainer what they focus on. If the answer is “all-around development,” that is not targeted enough. If the answer is “left foot and first touch in tight spaces,” that is a trainer who knows what they are doing.
Skills academies and extra team programs: be selective. A kid who is in four training environments per week is not developing four times faster than a kid in one.
Recovery, sleep, and physical development require time that overtraining consumes. At 11-12, two to three training sessions per week plus a game is a full week.
The signs that extra training is working: your kid asks for it. They practice at home without being told. They ask questions about things they worked on.
Training that a parent is pushing harder than the kid is pushing is not building a player. It is building a reason to qui