For engine failures in a light twin, doesn't the second engine take you to the crash scene?
As a USN Flight Instructor at NAS Milton (near Pensacola) I got my ATP in a Seneca I (checkride). A real "pig" on one engine. Would only climb 500'/min if 1/3 ball away and wing tilted toward good engine. If you can't do that, it may not fly level for long, either. As a former USN Pilot flying S2's with plenty of power, and other twins, this was a real eye opener!
Further, on my first takeoff (Seneca I) from Pensacola airport with the FAA Instructor, he pulled the mixture on the takeoff roll. Wow, I really didn't expect this, so of course I aborted the takeoff roll. I was so surprised he shut the engine down, I asked him if this was standard in the civilian world (certainly not in the military world I was used to). He said yes, and further, several others had attempted to fly on one engine. Of course these immediately failed the FAA Checkride.
Bottom line, you should practice single engine flying to stay proficient, etc. Not overconfident, but comfortable if it happens. I was very good single engine in the S2, C1, both aircraft with 9 cylinder 182o cubic inch engines. Plenty of power to climb and fly a while.
I have more stories, if you're interested.