Banks and crypto are two different world one is a fiat and the other is virtual,
That is where you all go wrong. Money may be physical or digital but it is still money and can be used.
if bank would create their own crypto how are they going to do that,
By using blockchain and hiring blockchain developers. You may not be aware but many financial institutions are already doing that for purposes other than developing a fiat backed currency. As humans we tend to forget that the people who run such companies are way ahead of common people's intellect.
bank is stable in value while crypto is not,
If you mean to say fiat is stable in price, then you mean to say that you are comparing bitcoin price against fiat and then coming to this conclusion. What if you were to think fiat price against bitcoin and use bitcoin as the base standard?
Then fiat would be equally volatile as bitcoin would be stable at 1btc.
how are they going to put ledger on it if the value of it is unstable, also in bitcoin they cannot control it, the reason why investor and people opted to use bitcoin is because they dont want others to control their money or what they invest.
Banks dont need to control people's money. The concept comes from governments starting their own stablecoins which is not a improbable idea. What is good about it is that law enforcement would be able to detect the money launderers if this is made a norm by monitoring the money going in and out of exchanges.
Only money launderers are the ones who oppose these concepts.