I think that as stated up earlier, the reason for initial thread failure is usually more than just a tension failure pulling out the threads. That face to face sliding action of the fastener thread to the threaded hole also has a galling and shearing action that helps cause the original failure.
Once the helicoil is inserted, the softer newly re-tapped STI hole and the helicoil are essentially stationary (and of a slightly larger OD) and the force of the insertion of the bolt is seen as much more of a tension with less of a shearing action at the original base metal. Now the shearing action is more between the fastener and the helicoil, which is inherently stronger and more gall resistant than the original base metal in most cases.
I think of it a bit in the same terms of why that same hole if assembled with a proper stud, tends to not pull threads as easily. The fastener being tightened is not rotating in the base metal, because the stud is essentially fixed rotation wise. The interface with that shear action is between the nut and the stud, both of which usually have higher strength.
Same kind of thought process of how using a washer under a bolt head or nut stops the shearing and galling of the item being clamped together. That action is happening on the face of the washer at the fastener instead.
Another item to consider is that both a helicoil and most commercially made external thread hardware are both formed threads, not cut. Those are inherently stronger than a cut thread as a lot of the stress raisers and microscopic surface tearing that cut threads create are not there on the interfacing/moving threads.
There are absolutely lots of cases where a tension failure alone occurs and a heilcoil or time-sert repair holds up far better in the long run. A big part of that is the fact that the new thread surface area is larger than the original. Particularly on thread insert styles that are not the helicoil type, as they are usually quite a bit bigger OD than the fastener they are holding.
Anyway, that's how my mind sees it.