Bitcoin anonymity - if all balances and transactions are openly visible, what are the implications 10 years from now for the average person using BTC as a savings account?

Fast forward 10 years... more people are using BTC as a savings account. But, my understanding is that this implies everyone's balances/transactions are public.

Will bitcoin implement more privacy measures, or will the world change how it perceives 'savings' accounts, such that the financial system actually becomes more open and transparent? If the latter, what are the implications in day to day life for someone holding BTC in a transparent and open 'savings' account?

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[EDIT] the question is for bitcoin to gain mass adoption, how will the average person who is non-technical get the same amount of privacy (from other members of the public) that they currently have with their bank savings account?