These are the questions that need to be asked.
You can.
> What part is the bank actually playing in this transaction?
They're lending you the money.
I assume you have some different, less obvious answers to this? If you're against the lending of money for interest, how about a halal mortgage? https://www.qardus.com/news/halal-mortgages-everything-you-n...
Practically speaking, not really. A tiny fraction of people might earn enough to save enough to buy a house, but most will be priced out at every stage by people taking mortgages. Some people inherit existing property and trade it for other property. But if you are starting from scratch it's virtually impossible. Do you know anyone who has done it?
> They're lending you the money.
Are they? If I lend you my car, I don't have access to my car during that time. But money is just made up. There's nothing moving around. Banks aren't losing anything when they lend you something. They just create a deposit and a liability and get on with it. As long as they are all doing it at roughly the same rate nothing stops the economy filling up on debt, as it has done and continues to do.
Remember, banks lending money is nothing like you or I lending money. The banks control the ledger. They don't play by the same rules as us.
I'm not sure are about states granting banks the right to create money. Do you have a source for this? As far as I can tell they do it simply because we all use them and trust them to keep the ledger. The state (meaning, the US or UK) doesn't seem to have much control over it.
The banks are obviously granted the limited right to create money by the government. Whether it's through regulation post facto or a charter a priori, by now virtually all modern states have a wide control over their banking systems, including setting required reserve rates.
> by now virtually all modern states have a wide control over their banking systems
This doesn't seem to be the case.
> including setting required reserve rates.
Can you find what the required reserve rate for the US and UK is? From what I can find the US does have a required rate but it's 0% and the UK doesn't have one at all.