Well then if the exposure can be controlled without a shutter, why have one? What is the benefit of augmenting an electronic device with a mechanical one, which will eventually fail?
Because the shutter allows some other tasks to be performed, like syncing the flash of light to the moment the front curtain is fully open, or to the instant the rear curtain begins to close.
Also features llike long exposure noise reduction require powering up the image sensor and making an equally long exposure with the shutter closed so the camera CPU can map the dark current noise of the image sensor.