Perhaps, as a "senior in economics at a business school", and FULL RESERVE BANKING without resorting to meaningless phrases like "CT-woo".
Gladly.
First. Flaw is not the right word. From dictionary.com....
1. a feature that mars the perfection of something; defect; fault: beauty without flaw; the flaws in our plan.
2. a defect impairing legal soundness or validity.
3. a crack, break, breach, or rent.
A system for organizing capital is not something that can be perfect. Also, any system short of magical pixie dust will probably be sound or valid. What the systems do have are general tradeoffs.
So, I will list some negative consequences of your proposals. I am not measuring the size of the negative aspects nor comparing them to the positives. That should be a big enough disclaimer.
Let us do full reserve banking. I mostly will assume a commodity currency. That is just more fun.
1) Assume a global world, there are some theories that foreign countries with central banks can economic rape a country with no monetary control.
2) Assume that is not an issue. As the economy grows, without inflation, prices will need to deflate. Humans do not deflate prices well and they tend to be sticky. Wages (a price like any other) tend to be sticky and more likely to lead to firings and depress economic growth. Also, it may cause economic growth to stall as people wait for prices to fall lower (perception that their wages will stick longer than the prices).
If not a commodity currency, there may be ways for the mint to put money in the economy. The methods have various issues with efficiency, welfare losses, transparency, etc. Another option is assuming that people may learn to renegotiate their wages every day. There are efficiency issues with that. Not to mention, it may involve people thinking beyond their monkey DNA, something not very common.
3) A bank would have to fund its operations. Fees would have to be assessed on depositors. People could use mattresses and we are back to ancient banking practices. The equilibrium price for banking services in this hypothetical world is giving me a hard-on. This thread has discussed that putting money in a bank leads to inflation reducing your wealth. In this scenario, putting money in a bank leads to fees reducing your wealth.
4) We still need a way to provide investment capital (or no investment capital allowed at all, another method for organizing our economy). So many options. The most obvious is the I-cant-believe-its-not-a-bank. Same setup we have now, just not called a bank.