How to prevent identification due to using exchange network addresses?

Hi,

exchange networks are nowadays the way how normal people get their hands on bitcoin. They buy them with fiat money, but have to give them their ID, address, name, etc. This compromises anonymity when making a withdrawal from those exchange networks: Every address you want them to send bitcoin to can now safely linked to your person. You kinda have to rely on them to not fuck up. They also often reuse addresses, so police people inspecting transaction history can clearly see that an address has received payout from an exchange network, and can then simply go hack ask them nicely about personal details.

My question is: How can I obfuscate this? What can a person do to still retain a maximum amount of anonymity after having an exchange network involved, without having to rely on third parties?