It is a reasonable question to ask (although even if the answer is No it may be hard to stop them - but that is a different issue).
Society has had anonymous cash for a very long time. My view is that it is important for cash to exist, and to be anonymous, and it is particularly important nowadays as the balance of power between government and citizen has tipped so much towards the government with modern technology.
Many societies are corrupt, authoritarian, kleptocratic or undemocratic. Not just Russia and China but many more such as Myanmar, Saudi Arabia, Venezuela, Zimbabwe, Turkey. Even, under its current government, India.
So, I believe that it is important that anonymous cash, not tracked by government, exists. As more critical functions (such as a journalist paying an online source for information regarding crimes by the government) move to the digital world, that means anonymous digital cash as well. Bitcoin, etc are not anonymous - every transaction is public and is recorded forever.
So, I believe mixers need to exist. Authorities should focus on closing down the ones which handle very large amounts of money - but making sure that facilities still exist for mixing moderate amounts.