* A high-wing aircraft has stacks of space under the wings for engines.
true
* A high-wing aircraft has "natural roll-stability" as the G of G is under the Centre of Lift, and will "want to" fly level (we use dihedral on aircraft to encourage just this behaviour)
That's not exactly how dihedral effect works 
Conversely, a simple high wing configuration can have too much dihedral stability, especially on a swept wing, and can require (considerable) amounts of dihedral as a result. This can actually make the tip more at risk of ground strike than a low wing type, where the dihedral helps keep the tip out of harnm's way
* A high-wing aircraft can have the stabilisers mounted where they are very unlikely to be in the wing shadow, and might have their efficiency enhanced by the higher-velocity air emanating from the engine efflux.
Engine efflux hitting anything is usually a bad idea - from a structural fatigue point of view.
* A high-wing aircraft gives pax and crew a better view of the ground.
* Higher engines would be less likely to suffer FOD, especially during reverse thrust.
* A high wing would probably be less likely to be damaged by apron vehicles driving into it (for large aircraft)
all three true to one extent or another
(-) Admittedly, the engines on a high-wing are unlikely to be so low as to be below the G of G, and therefor would not produce the same pitch-up force when accelerating (usually what is needed at that time - TOGA, emergencies) - in fact, would probably produce a pitch-down moment, not always good
Some additional concerns with a high wing:
Harder to deice or confirm clear of ice, since you can't see much of the upper surface ewxcept from a lift of some kind.
Forces the undercarraige to be fuselage mounted (= narrow track, may be a stability issue, plus probably some kind of undercarraige fairing) or to be very long and 'stalky' - which may have loads problems for the gear. And, being longer, it's harder to fit into a reasonable bay size.
Being further out of ground effect, it MAY be less efficient for takeoff/landing.