Actually you can make a personal wallet that is not associated with any account and not publish it. One disadvantage of bitcoin will be replaced with other advantages.
Tracing transaction of bitcoin isn't disadvantage really. Have you ever thought that if there is no transaction id then how will you prove that you have sent bitcoin to the receiver? Actually problem is reveal your address to public, otherwise transaction details still will keep your anonymity since anyone don't know who is the behind of this transaction except sender and receiver. To keep safe your privacy, don't share your receiving/sending address with any third person and you should always create new address for receive bitcoin. If you need more privacy then I will suggest use any bitcoin mixer to hide your identity.