It IS a big strong subframe, that's how monocoque construction works. You have front and rear frame rails, they are connected to the floor, and connected to the rocker panels via the floorpan and torque boxes - effectively a perimeter frame integral to the body structure.
Body on frame provides strength and isolation, NOT stiffness. The separate frame can twist bend and distort while the body atop is basically along for the ride on rubber pucks. The push for safety, effeciency and performance rendered this style of construction obsolete in all but trucks, where isolation and sheer strength is still the biggest selling point.