Banning all activities after one accident is throwing the baby out with the bathwater.
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From 吕氏春秋·荡兵 (Warring States): 夫有以噎死者,欲禁天下之食,悖 - 'because one person choked to death, someone wants to forbid eating under heaven, this is absurd.' The philosopher's point: don't abolish a whole practice because of a single mishap. The idiom preserves the argument almost verbatim.
usage
Standard rhetorical move against overreaction, in policy debates, management, parenting. Almost always used to criticize someone else's excessive caution. Close English: 'throwing out the baby with the bathwater.'