Will you send your docs in KYC case?
Depends on who's asking for your KYC, shady exchanges? NO, ICO or projects? NO.
Do you think that it really helps to find illegal activities?
I think it's based on the premises that it can deter illegal activities because once authorities identify those address related to someone whose involved in criminality and then he cashes it out in a exchange that requires KYC then he could simply be arrested. That is if exchanges cooperate or shall I say harass and 'force' to give all the details because of AML.