The mixed grip should only be used by competitive powerlifters and only in the specific or pre-competition phase. Most of the year they should deadlift with a double pronated (overhand) or hook grip. Even using straps from time to time is fine.

If you're only training to improve your appearance, gain muscle, and get stronger and you have no intention of competing, then there's nothing wrong with using straps for most of your heavy deadlift work. It's much better than using a mixed grip.

I've worked with a female powerlifter who developed a lower back and hip issue from the mixed grip, and there's also the potential it has to cause problems for your biceps.

The Main Problem

With the mixed grip you'll have a natural tendency to rotate your torso/hips toward the supinated (underhand grip) side. In other words, you'll tend to push forward with the supinated side and pull back with the pronated one.

The supinated side will also tend to stay a bit higher than the pronated side, which will more easily hang down. It'll be much easier to engage the lat on the pronated than supinated side which can make the lift unbalanced. And finally, the biceps on the supinated side will be in a much more dangerous position for a tear.

Yes, the mixed grip allows you to hold bigger weights. So if you're competing in powerlifting it'll be necessary to use in competition. And if you use it in competition, you'll need to practice it because it feels different than a double pronated grip.

But even for competitors, the double pronated grip is a better option for most of your training. It's safer and will make your grip stronger. If grip is an issue, you can learn to use the hook grip, which is as strong as the mixed grip once you get comfortable with it:

Hook Grip 1
Hook Grip 2

Use the mixed grip only on the last 4 weeks prior to your competition, and ideally, switch arms every set to avoid creating an imbalance.

Related:  The 5 Most Dangerous Deadlift Mistakes

Related:  Deadlift Barefoot. Here's Why.