Yes, but the exchange must comply with government regulations , so we need to have different exchange in different country just to make that possible.

Other problem is security of the money deposit in that particular exchange government already know that exchange is prone with hacking .another thing they need to also prepare a lot of cash ready to widraw any time that  there are persons want to cash out in Fiat. As you said you don't want to have banks then the exchange should provide that.