TJ will probably chime in but I think climbing Katahdin via Hunt Trail is not a place for little kids. In many places it is nearly vertical with rod iron handholds. The handholds may have been built for adults and not very short people. Plenty of places for little kids to trip and fall. Then once you make it to the Table Land you could get immediately hit by high winds. Suddenly you are above the tree line at a place where wind has the opportunity to accelerate. Turning around and descending on this trail could be even harder for little kids. Added to the complexity BSP is remote. It's not the same as hiking Mt.Washington with several bailout points and a quick return to the convenience of civilization, electricity and waiting ambulance.
Now that I have said that ... my first son climbed Katahdin with me via Pamola Peak, Knife Edge when he was around 7. I had a few safety items with me (rope) and he had the experience of doing the Presi a year earlier and probably 30 peaks under his belt.