Why can't I just cut off the faucet connection and connect the hoses with hose couplings and hose clamps to hot water and waste?

To a certain extent you can do what you describe but it isn't the best installation and would not meet code. Right npow you have a double hose manifold that goes to your sink for supply and drain. How did you picture and open line for you to slip on your old rubber hose supply? If you have to create a line then just run a copper line all the way to the washers fill solenoid. The drain needs to make a high loop or air gap and then connect to an existing sink drain that's trapped or a whole new drain and trap. Don't forget to remove the casters since you do not want this to move. Not quite as simple as you first pictured?