I'm not worried about law enforcement, just regular snoopers who would be unable to force Coinbase to turnover data. How could a person link the transactions, they can only see that they came from Coinbase but cannot see which of the millions of Coinbase users sent it and cannot see that these transactions came from the same user. Am I wrong about this?
You are right, the "average Joe" will have a hard time to find the connection on their own they have to get a court order or something like that. However there are two problems you will face in the future.
1. When Coinbase gets hacked (not a matter of if, but when) their database could be published by the hacker and it would be free for everyone to see. It may even end up one some chain-analysis website like walletexplorer.com where people can easily search an address and see all the linked transactions.
2. When you end up sending bitcoin to a destination that breaks Coinbase's ToS and they shut down your account and seize your funds.
Thanks. So what is the best solution?