You're making the assumption that AT only controls speed. In a Boeing at least, the AFDS is a very complex system with a multitude of modes, many of which rarely get used.
For most of the descent the thrust should be at idle, with the speed controlled by elevator. In the final stages of the approach other modes may come into play such as ALT HOLD, V/S, FLCH, SPD PATH (both geometric and approach) etc... but that all happens as part of an integrated system with AP or FD. In a Boeing, when you turn off the AP you turn off the AT as well and, you know... fly the airplane.