If the motor coupler is broken it will not agitate or spin. At all. It will, however pump water out just fine.
If there is really some water (not just really wet clothes) in the bottom of the tub when the cycle is done there is an obstruction somewhere in the drain line or pump. One of the possible causes for this is a rogue sock or handkechief that has leapt into the space between the basket and outer tub that sometimes manages to clog the water outlet at the bottom of the tub.
IF it's just really wet clothes in the bottom of the tub it's most likely the spin clutch.
The spin clutch is not at all difficult to replace. You do have to remove the agitator, put the machine on its side or front and pull out the whole drive mechanism. But on DD machines that is really only about a 10-15 minute job. The clutch sits on top of the drive mechanism and switches out in 5 minutes and then it takes another 10 minutes to put everything back together.