In the jet world, multiengine ops become easier again, as the airplane is less trying to kill you in the event of a failure (much lower drag from a failed engine, no runaway prop concerns, less yaw from asymmetric thrust) and you have massive amounts of surplus power at low altitude. There are situations in a jet where you can lose an engine on the takeoff roll, even prior to lifting the nosewheel, and for the safest course of action to be to continue the takeoff, take the problem airborne, and consider a return or divert in the air. (Failures after V1 ["takeoff decision speed"] and before Vr ["rotate"].) There are no such times in the piston or (edit to add: light) turboprop world.
The safety rates and reasons are frequently debated. As a pilot who frequently flies my family around and is strongly disinterested in making the numerator part of the statistics, I read every NTSB fatal, every crash of the types I fly, and most of the serious crashes of other types.
My thoughts are that the pilots are, by a wide margin, the weakest link in general aviation (non-military, non-commercial) piston singles, making poor decisions on fuel, weather, and other dispatch-related topics. I'd bet that 3/4ths of the piston single fatals have pilot or dispatch (also pilot) as the root cause, not engine or mechanical.