The issue is not the attitude of the aircraft, but rather its full maneuver state. You picture it upside down, and the rotors now having to lift upside down, but that is not what happens, in most cases.
In the loops and split S maneuvers we do, the aircraft is continuously developing some positive load factor with the rotor pulling it toward the earth, so that the pilot feels normal in his seat, and a glass of water on the dash would not spill. They can be done in most helos, but with tiny margins for error in many.
Two exceptions are the BO-105 and Comanche., Both have very controllable rotors, and can develop significant negative lift. In films, I have seen the BO pushed over to 135 degrees nose down and then just pulled back up to level. This surely created lots of negative G. These two helos come closest to your concept of true, trimmed upside down flight.
Of course, control is only part of the issue. Without inverted fuel and hydraulic systems, these helos would get very quiet after a few seconds upside down!