Had a client recently send me some lifting videos. In the video, I noticed this person was doing some barbell work with a mixed grip (one hand under, one over) but was still using straps.
The point of using straps is to be able to hold on to the weight while still using a double over hand. (Most people can hold less using a double overhand, unless they are using a hook grip).
There is a time and place to use straps. If you are doing back work, stiff leggeds, RDL's and other exercises where the weight of the bar is not important, then use straps. It will be less torque on your back and keep you in a solid and straight position.
If you planning to compete in powerlifting, then I would NOT use them for regular deadlifts, only because you need to be able to deadlift without them in a meet.
Now, some people use them for heavy rack or block pulls or other variations, but typically these are people that have already built a strong enough grip and these exercises are done as supplemental to their deadlift.
Bodybuilders, who are not competing in powerlifting, often use straps for their deadlifts. Again, for them, they aren't concerned about holding on to the bar. They don't want to bothered with their grip when the focus is on their back work.
I've heard people make comments like "Maybe he shouldn't be lifting it if he can't hold onto it" (in regards to a bodybuilder deadlifting a pretty decent weight for reps. Well, holding on to the bar is not his focus. He's not competing in a deadlift comp and wants the mind/muscle connection to be on his back/hamstrings, etc and not his grip.
Straps don't make a person lift more than they are strong enough for. If I put straps on and try to pull 500, it won't happen no matter what. So these people are still strong enough to pull the weight, it just all depends on what their focus is.