The most dangerous place to have a failure is during initial take off (low hour student pilot here). The engine kicking on would give you a chance to actually do what is nearly impossible in this circumstance, get back to the airport safely without a stall.
As I understand usually the most dangerous circumstances are the one above described, stalling on base or final approach to runway and flying from VFR (clear of clouds with visibility) into IMC poor weather conditions.
Both of those circumstances wouldn't benefit from a backup engine. : (
As other people in the threads have posted, Fuel Starvation, water condensation in the fuel, some of those situations this would definitely help, but all of those conditions are 100% preventable with proper pre-flight planning and inspections.