Your idea is exactly the way the economy already works. People deposit their money in a bank, they receive an evidence of deposit in return (their bank balance), and then banks then lend the deposited money out to businesses (or individuals) that can use it. When people buy something (say with a credit card), the evidence of deposit is transferred to the seller's bank account electronically, so they don't have to handle paper certificates. It is true that we have cash (dollar bills) but these are mostly used as a convenient way to transport small amounts of money between bank accounts where it will reside (very few people keep any significant fraction of their cash as physical dollar bills.)

You're essentially proposing to open a socially conscious bank that promises to only give loans to socially conscious organizations (and presumably gives them a lower than market interest rate, at the expense of either lower interest rates to depositors, or charging depositors higher fees.) That part's reasonable. I used to keep my money in a bank that worked sort of like that. They tend to be a hard sell because they don't have a lot of ATMs, they don't pay good interest rates, they don't have super slick online banking.. all the forces that have caused consolidation in retail banking work against them. Eventually I decided that I'd use the bank that best served my banking needs, and separately donate to whatever organizations I personally wanted to support, rather than trying to couple the two and thus do both of them inefficiently.

You also propose to charge people a punitive fee if they ever withdraw their money from your bank, for example to do business with someone that doesn't have an account at your bank (which will be most people, to start with.) I don't think anyone wants to deposit their money at a bank like that. I sure don't.

If you want to get people to use your bank, I think that at the end of the day, you're going to have to actually make your bank an attractive place to keep deposits. I think it's really going to be an uphill battle to get people to opt in to these anticompetitive/protectionist provisions that keep money in your bank, because the instant they do it, their dollars become less valuable. They'd do better to donate to a charity directly.

So, your idea stinks because if you want to do this, you should just open a bank and focus on lending to organizations you like, and do everything you can to attract depositors (and imposing a tax when they give money to someone not at your bank is probably going to hurt you more than it helps, in terms of attracting depositors.) And, it turns out a lot of people have already had this idea, and they're called credit unions. There is a clean regulatory framework around them, you will have deposit insurance (the credit union equivalent of the FDIC), and you might be surprised how easy they are to start (not trivial, but easier than banks for sure.)