Several things. I use straps the other way. (the strap runs with the thumb). I should say "used to" as now I use versa grips.
Yes I am a big believer in straps and any dead training over 2 reps, I use straps. Several reasons. First and foremost, I like to do most of my deadlifting DOH as it activates both lats equally. It also takes away the risk of bicep rupture on the underhand grip arm. I have a decent deadlift for a smaller guy and never have a problem switching to mixed and pulling when I want to do a "real" deadlift. Not being purely a power lifter though, I dont want miss the benefits of a DOH deadlift in my back fullness.
I also use them (at times) where grip would never be an issue. Eg lat pulldns or pullups when I am really wanting to target the lats. Reason is when you flex you hand to grip, you are inadvertently activating muscles in the forearm and bicep which assist in pulling. With straps, the relaxation of the hand allows one to focus more on pulling with the lats. So those times I am looking to do that, I use straps. I also do them without when I am looking to move max weight for the tension stimulation it gives. All different tools in the shed and for me, straps are a great one.