An insurmountable problem is heat. The shuttle had radiators in the cargo doors. It could not stay up if doors were not opened. The ISS has radiators.
ST never addressed the issue. Even at 99.9% efficient the waste heat of the power source would cook the crew. Place a box filled with air in deep space. Turn on a power source and the temperature will rise if the power exceeds the radiation from the box. It will keep rising until something failed.
It's a problem that must be accounted for, for sure; But, as the radiators on the ISS and in the shuttle's cargo doors demonstrate, it is not an insurmountable problem.
It's not insurmountable at the energy levels we operate at.
At Trek-level energy levels it is.