If you let dirty water fill up your tub while you shower that'll result in a dirty ring around your bathtub which you'll have to clean... with more water (and p

If you let dirty water fill up your tub while you shower that'll result in a dirty ring around your bathtub which you'll have to clean... with more water (and possibly chemicals)... it'll cost you extra time to clean as well. All together the total costs of the extra cleaning resulting from this may exceed the cost savings from letting the water heat your home.