This is likely just a mistake on the shop's part. Using a t-nut (they go by some other names) to repair hanger threads used to be very common. They're faster, although that's about the only advantage. I don't know that they fell out of favor because of interference issues like you describe, but it is certainly a possibility with them on modern bikes.
One way a shop could have gotten to this plan is simply not having an M10x1 helicoil kit. Another is if the damage to the threads was larger than the tap in the M10 kit (11.4mm major diameter according to this, I don't have one in front of me), but the nut type approach was able to work since you use a 12mm drill bit to install them.
If the 11.4mm number is correct and you have a 12mm hole in the hanger now, then it is impossible to simply switch to a coil insert. What may be possible is switching to a solid-wall insert such as EZ-Lok, which require a larger hole (the special tap for them is larger diameter) than coil inserts. There are a few different lines out there of products like this. The constraining factor for you in this case is how much material is left in the hanger to cut the threads for the solid-wall insert. If this is a steel bike and you're already at 12mm, there may not be enough left. Aluminum bikes with integral hangers often were built chunkier there, so you could be in luck. If you go with a solid-wall insert, its depth (thickness) will likely need to be modified to match that of the hanger exactly, so that you don't wind up with the same problem again.
On some bikes it could work in your situation to simply relieve some material off the inside of the hanger to make room for the back of the nutted insert. This would mostly be if it was an early aluminum bike and the hanger was very thick. There would likely be no way of making this work on a steel bike.
If it's steel, there are various hot repairs that would fix everything (new hanger, new dropout, build up the area with brass and retap it, braze in a piece of nutted insert, etc), but this is a hassle. Since the strength requirements are fairly low, it could also work to take the insert, cut off the wrench flats, and epoxy it in. Done right I see no problem with that.