If the above is true, are there any legitimate (I know this is subjective) exchanges that do not keep identities of their customers? I have heard of local meetups, but that does not seem very convenient and there are trust issues.
Are you sure there is any exchange asking for people identity? Because for me, I can easily trade coins without any type of verification.
However, when one need to sold Bitcoin to native currency then one need to provide his/her complete identity like bank account, etc. collectively known as KYC (Know your customer) due to Income Tax requirements but there is hardly any requirement on exchanges. This is true triumph of cryptocurrency