Bank's don't have that model. Any sane person would have a separate savings account that doesn't really get used. The checking account is meant for variable balances, because your account number is more than likely floating around via checks/online ACH transfers which results in the potential for a security breach.
So then why don't they just call it a savings account and a checking account? Wallet is an implementation detail at this point that the average user shouldn't have to learn when there's already a word in their vocabulary.
