Well, privacy has to be gamble. If I do something, I leave a trace. I might directly interact with someone (buying drugs, for instance) or it might be in the privacy of my own room. But I'm always gambling that (a) anyone who I interact with won't dob me in and (b) no third party will detect my actions.
Obviously I hope my bank keeps a record of my assets with them. Perhaps they could merely keep my assets sealed in a box identified with a code and locked by a key, and they cannot open the box without the key, and I keep the only copy of that key. Perhaps the box is an encrypted database record and the key is a nice megabyte long random number which takes an hour to confirm. I can suppose it's secure (for the time being). And it's formally anonymous, since they don't even record that I posses the key.
But I still leave a trace when I access it. It's an intrinsic risk. I also risk dying every time I walk out of my house. I do things that have risk involved because it is necessary. Risk is not an argument against an activity.
I just want some privacy.