The vast majority of mid airs are near airports. Your device will help
you away from airports, but I wonder how much help it will be near
airports. Also, it helps to be aware of how the IFR approaches interact
with the VFR pattern because sometimes they conflict.

The big sky theory WILL protect you a lot away from airports. Helps
even in close. We've all had close calls though. (I've had 3 and they
were all either in the pattern (2), or on the "normal" approach path 5
miles or so out. The device you have would have helped with the 5 miles
out one.