With a Bitcoin wallet, have a great advantage towards a bank account, for many reasons. Those are the ones that helped me choose a Bitcoin wallet over a bank account (although sometimes it is necessary to have a bank account as well).
The reasons are the following:
1. Lower fees than banks
2. Total control of your funds
3. Send and/or receive money almost instantly.
4. No limits or restrictions on the amount of money I deposit into.
5. And no central authority.
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6. There is no problem of nominations to inherit to your next generation.
7. No annual fee or maintenance fee or any penalties
8. Can have unlimited accounts (address/wallet) to make some special accounts like retirement account.
9. No account opening hassles. Get a bitcoin address instantly.
10. International fund transfer facility and safety locker facility (cold storage) are free and instant.