Why insane? None of the outputs from this section of the power supply are correct, and there are some burned parts. Any/all of the parts I mentioned could be bad, and replacing some of the parts and leaving other bad parts still in the circuit could result in those new parts frying again. Better to check them all the first time through. As for the 2 10W resistors.... The schematic indicates a 1/4 W resistor, and a 4.7 ohm 1/4W resistor will handle 200 mA or so. Should be sufficient. It does look like they are using that resistor as a safety fuse in the circuit, so replacing with the proper part is a safety related repair. 'I' might put a 1/2W resistor there, but I won't tell anyone else to do so.
Why are they there? Might be all the previous 'tech' had, or the original 4.7 ohm may have failed because something downstream is drawing too much current, and rather than fix downstream a high wattage resistor was used - kind of like wrapping a fuse in aluminum foil because the specified part keeps blowing.