Great answer, Chaim.
You are completely right about the potential dangers of fractional reserve banking. Furthermore, it drives the business cycle by affecting interest rates and thereby creating an illusion of having more saved recourses to be used for large projects during the period of artificial economic growth in the years before the inevitable recession hits. Because of this, I think that the practice should be outlawed entirely.
Lending would still be possible under a full reserve system. For as you say, lending is a necessity. The 100% reserve would only be required for demand deposits. There would still be created loans from time deposits. The problem with fractional reserve banking is the creation of loans from demand deposits. This, of course, is contrary to the original purpose and nature of demand deposits.