User blog comment:Yatanogarasu/Children Inherit Parents' Legacy/@comment-3119203-20110301044152

This goes with relatives too: a guy i know has a brother who is really smart and is several years older than he is, and everyone expects him to live up to his brothers reputation.

As for your question, i believe no. I child is not their parents, as shown by sabo, and they did none of the crimes their parents committed. Kids cant choose their parents. Ace and luffy deserved their bounties for their actions, but robins was unfair. So what if they inherit their parents tendencies? arrest them for what they do, not for what they might do later on because there is a chance that they could be like their father