The simple answer is that variants work sections/aspects of the movement in order to strengthen the movement as a whole.
If you keep pounding away at deadlifts and are stuck in a rut, then its probably a good idea to sitdown and figure out what is stopping your progress. Then you can address specific concerns within the movement you want to improve. An even better approach (imo) is to be pro-active and use variants as a staple with the big lifts appearing less frequently. Of course I'm referring to people that have a couple/few years of serious training and can't linearly progress on a 5x5 every week
There's nothing/noone saying that you can't do the big compounds in your routine. In fact I would encourage that you do them from time to time, especially if you're doing variations that are meant to enhance your ability in them
"When you complete the program you will be amazed by the amount of weight you are able to bench-press, squat, deadlift, and chinup after just 16 weeks of focused training" That's a quote I pulled from Maximum Strength, the whole point of it is to show the benefit of doing more than just hammering away at the big lifts.
You'd be surprised at how much you can increase your squat, deadlift, bench, etc. without actually doing them.
Sounds pretty odd to say that you can increase your back squat by not doing them