Correct me if I am wrong, but my understanding of this battery packs discussion is;
When you connect the batteries. The higher voltage from the higher voltage battery flows to the lower voltage. Like water and a siphon hose between 2 buckets, they will continue to flow until they are level. If you were to connect the jumper battery for a while before cranking on the starter. The lower voltage battery would increase (rise) to bring up the battery. Then the heavy combined amp draw would not be put on the jumper battery, but split between the 2 batteries. This would reduce the the draw on the jumper pack when cranking on the starter.
The quick connect and crank of the batteries and run the starter motor as well, right off the get-go, the jumper battery is trying to bring up the charge of the dead battery and start it at the same time. This is a big drain for the smaller lithium packs wires and can be to much draw for the (as was pointed out (2 gage wire)) wire to handle. In my view this could be a operator mistake. Would the quick connect method work if the original battery was partly charged or a small engine not needing that much power to kick over the motor? There is a good chance it will work. For a heavily discharged battery and a larger engine, maybe not.