I will be very impressed if this is capable of giving us teeth that align well without having to get braces as soon as they come in. When they're developing as a child, it's alongside the rest of the face and jaw, so everything is guided and fit together. Having them come in separately might not work the same, whether they're able to regrow a single tooth or a full set. I would expect it to also cause wisdom teeth to regrow, which would be a problem. This doesn't seem to be a targeted growth. They just inject it into the body and wait to see if any teeth grow, so I don't understand how they can give it to humans who have any existing teeth without a whole new set growing and pushing those out, or coming out sideways underneath them. Perhaps having an existing tooth somehow inhibits the regrowth, but I wonder how something like having had a root canal would affect it.
The animals like alligators and sharks that completely regrow teeth have an entirely different arrangement of teeth, with a completely different shape and function from human, which is far more forgiving of misalignments. When you're just stabbing the food and tearing it apart, a jagged bite isn't a big deal and even helps. When you're grinding vegetable matter and need things to squeeze relatively flat, those teeth need to grow in a pretty specific way. I suspect this may be WHY some species lost the ability to grow new teeth after birth. (There are species that have teeth that continuously grow, like rabbits, but those are not NEW teeth, and they have to constantly wear them down or it will kill them.)
They show a ferret that grew an extra front tooth, like that's a good thing. We don't want humans just randomly growing extra teeth. And ferrets and other animals aren't concerned with the appearance of their teeth so if they aren't straight, it doesn't matter, as long as it doesn't negatively affect their ability to eat.