There is, in fact. Baumol's Cost Disease, and it's a real bitch.
Manufacturing has compounding productivity gains - one worker today produces vastly more than one worker in 1950. Elderly care doesn't. You can't make a caregiver 10x more productive through better tooling. The productivity ceiling is fixed by the nature of the work.
Wages across sectors compete for workers. So service-sector wages only rise when they have to bid workers away from high-productivity sectors. This predicts: service wages are borrowed from productivity gains elsewhere in the economy.
This doesn't mean we shouldn't want caregivers paid well. It means wanting isn't a mechanism. The mechanism is productivity growth in tradeable sectors pulling wages up economy-wide.