I think buying with cash and from individuals is more private and will cost less.
I agree, but the problem is finding a trusted person, especially when it comes to larger amounts - no one should walk with thousands of $ in their pocket, and also not have a larger amount of BTC in some hot wallet on a smartphone. If there is an option for crypto ATM, perhaps it could be considered, although in that case a fee of at least 5% or more should be expected.
Of course, only if the ATM does not require the user to be verified in any other way than SMS - and this anonymity can be achieved if we do not use a number associated with our real identity.