Even in countries with KYC laws, it should be perfectly legal to have crypto exchange. Since there is no FIAT involed it cannot be used for money laundering per say.
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You said it, it should be perfectly legal to operate a crypto exchange, and if it is legal, then you are subject to submit to the regulations because you are making money out of it, just in the form of cryptocurrencies. A business should submit to these legal rules to continue operating. Also, aren't you aware that bitcoin can be a medium for money laundering because it has value? Money laundering isn't exclusive to fiat only.