But I wonder if anyone's ever tried.
I have personally and I have seen other check airmen and instructors do the same at various 121 carriers here in the US. They all have heard the same answer:
"Train to the training program minimum hours, it's what we're budgeted for. If the FAA thought we'd need more to be safe they would require that we increase the hours in the training program."
The FAA when asked about it says:
"We only hold the minimum standard, it's up to the operator to go beyond that."