However, this is actually not applicable most of the times, because they have so inferior grip, that you keep overworking them much more than you would soft tires and that's actually what causes most of the wear.
The result is that in most circumstances, soft tires last acually longer, especially if you save them and keep from skidding and squeeling. Even if you don't overwork them, you can still keep better pace than with hard tires driven aggressively.
So, generally you are right.