The NTSB has frequent accounts of fatalities where after engine problems they didn’t reach the runway. Some from the circuit.
( And one where ATC directed the pilot to an airfield which still existed on their database, but had been built-over.)
There are big differences in the height above ground we fly, and the likelyhood of a good outcome from a hillside landing, depending on manoeuvrability and stall speed. So the answers will differ.
The requirement to fly a circuit, often insisted upon by instructors in PFLs, is in my opinion, crazy.
The advantages are not negligeable actually: judging height, inspecting the field, falling back into an automated pattern.
