Hi Tolu, for me privacy and anonymity are different things which serves different purposes.
When we are talk about privacy, we are referring to a situation where the identity of the user is known but what the user does or doing is protected or not known. You can say that the user’s data is protected from the public eyes.
Then, when it comes to anonymity, we are referring to a situation where the the identity of the user is protected and not known but what he does is seen. That’s where tools like tor and VPN comes in, to hide our identity but people will still see what we did on the internet but they won’t know who did it.
If you are talking about preserving our privacy better then that’s where encryption comes in and it should be a very strong encryption at that in order to protect and encrypt users data better.
For your second question, I don’t believe that privacy is more important when it comes to a case of using the privacy to commit crimes like money laundering and terrorist activities. Apart from such scenarios, privacy is very important and should be protected.