I could be wrong, but I have never thought using the ground on a bike frame was a good idea. To me, a direct ground to the battery is superior. But, if I am wrong, there are no consequences in this instance.
I guess someone could do a voltage drop comparison and that might make this old dog change his mind.
However, if the replacement connector overheats that ground circuit again, it would mean that the factory ground provision is insufficient for some reason on my bike. Running a new ground wire to the factory front ground point would probably remedy that, but a ground to the battery would be somewhat more effective.
BTW, it might not be material to Ducatis, but I have greatly improved headlight effectiveness on other bikes by running new direct grounds to each socket.