You are right - this will be a strong incentive to keep as little as possible in a checking account, and either lend or invest the rest. There are two main differences from the current system:
1. Depositors will have to explicitly give up/lock their funds for a set period of time if the funds are to be lent out and they are to earn interest. Early withdrawals come with a significant fee. This makes bank runs very unlikely, eliminating the need for a central bank. The longer you want to lend the money for, the higher the interest. But you can also lend money overnight.
2. No money creation, leading to proper alignment of time preferences of investors/consumers and businesses. Interest rates correctly reflect this time preference. If money represents a claim on real resources, then a business can only use as many of these resources for investment as consumers are willing to forego consuming. Interest rates reflect the actual supply and demand of resources/consumption at different time horizons and do not get artificially "set" or otherwise manipulated.
Because of these two properties, the boom-bust leverage cycle is greatly dampened, if not completely eliminated.