Competition can be useful at U11, but it should not be the atmosphere of every minute.
If every activity has a score, consequence, race or winner, some children start to feel that training is another performance they are being judged on rather than somewhere they can experiment and learn. The fact he still enjoys matches but finds training stressful is worth listening to.
I would want a good week to contain different types of challenge: competitive games, technical work, problem-solving, free play and moments where players can try something without worrying about the outcome.
Competition itself is not the problem. The question is whether it is helping the child become more engaged and resilient, or simply making them anxious about making mistakes.
I would speak to the coaches calmly rather than asking them to remove competition. Explain what he is saying and ask how they balance challenge with enjoyment.
At U11, players should experience pressure sometimes. They should not feel under pressure all the time.