Well I’m certainly no “expert” in Austrian economics, but I have studied it for awhile and think I have a reasonable grasp on the concepts. I would say the mode of operation you have outlined is correct, there is nothing wrong with depositors freely depositing funds for reasons they find beneficial and for banks to lend said funds out for reasons beneficial to them and their depositors. The problem with fractional reserve lending is not the “fractionality” per se but rather the fact that the funds lent out are not then also restricted from withdrawal by the depositors… which ultimately causes all the lending to become an inflationary bubble. For example, under the current system if I deposit $100 into the bank, the bank can then lend out $90 of that… however I can also come and withdraw all $100 as well… so now you have two actors in the economy spending $100 and $90… the $90 being created out of thin air.
A non-inflationary lending scenario would be one whereby I agree to deposit the $100 for x period and I understand I may not withdraw those funds. Period. Which is basically what we have with CD’s (time deposits)… that would be an example of “proper” non-inflationary lending. The bank earns interest and the depositor earns interest as well, the only tradeoff is they can’t use the funds. In a sense, the depositor is lending the funds and using the bank as broker to handle all the messy details and for the service of handling the messy details the bank gets to take a cut of the interest rate paid to the depositor (the actual lender of funds).
There are different ways this could be structured, say I want to deposit $10,000 but only commit half of it to such lending, that way I could have some of my money pay me income to cover the costs of having the bank store the other $5000 for me so I can use it as I need to whenever I need to.
Without any lending being done then depositors would pay the bank for the services provided (store-housing, check clearing, etc). It’s all up to the individual to decide whether they want to pay for the service or get it for “free” by committing some set amount of funds to be tied up for some set period of time.