Exchanges are regulated so they are asking for ID and photos, these days they're even taking screen shots of your face for transactions.
Blockchain wallet doesn't ask for any form of ID, not even your phone number if you're only using it as a wallet, but if you're buying then you run into the same trouble of having to ID yourself.
There are few ways of getting around this ID problem, this is why we suggest at least a couple jumping off points before you use crypto to transact and if you're really into hiding your transaction using Monero. You still need new wallets for every transaction so you don't have a long record of transactions in one place.
Using a bank account that isn't attached to any other transactions except crypto and one you only deposit cash(never use a check) will allow you to close out these accounts to hide your trail as the years go by. You don't want to buy crypto with your family account, it will be there on your statement. Sort of like the reason to use PO Box for shipments as you close them out and move onto other locations so you don't have a long history.