Why does "let" suggests that he simply failed to obstruct their dancing? "let" is like "allow". We allow someone to do something.
"John let the children dance
let suggests that he simply failed to obstruct their dancing (though he might have)"
John let the children dance. ~ The children were dancing, but John did not stop them from dancing. "failed to obstruct" is a little too strong, in my opinion.
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John let the children dance.
~ The children were dancing, but John did not stop them from dancing.
"failed to obstruct" is a little too strong, in my opinion. It suggests an attempt to obstruct (=stop) the dancing, and the sentence John let the children dance does not imply that John tried to stop their dancing.
CJ