You’re right that almost all of today’s banks use fractional reserve practices. Although e-gold and the like might not.
The problem is that governments step in on banks’ behalf when a bank run occurs. If justice were to be served, then the banks that did not have their despositor’s money, all of it, when he came asking for it that bank would be found guilty of fraud. Instead governments call “Bank Holidays” or their buddies at the Central Bank bail out the bank that lent out the depositor’s savings.
A proper lending bank would be one that lends out only money which has been provided for just that purpose. A certificate of deposit might be that means, rather than a savings account.
There’s a difference between a demand deposit (a current account) and a time deposit (a savings account).
A demand deposit is where the bank’s function is to safeguard your money, and that is it. Since money is a fungible good, for the purpose of convenience you transfer ownership, but not availability.
A time deposit is a contract between you and the bank that transfers both ownership and availability of your money to the bank, for a set period of time. The bank can then loan this out to anyone it wants.
A bank operating without fractional reserve banking would hold 100% of its demand deposits, while lending out only time deposits. Since the bank has availability of your time deposits for the duration of the contract, bank runs are impossible since you have no contractual rights to take back your money until the time expires.
So yes, it’s perfectly feasible to operate under a full reserve while still making a profit.
One thing that would really help you is to not make reference to the right to ‘life’, since it may be vague. Rothbard preferred right to ‘self ownership’, which brings the matter back to the roots of the ‘negative’ aspect of natural rights in that they do not impose obligations on others.