I think the main issue is wing flutter. Missing (part of) an engine will significantly change the eigenfrequencies of the wing and could lead to all sorts of nasty bending and torsion problems in flight.
The CoG issue can be compensated for with fuel and ballast and the missing drag should be well compensated for by the missing thrust.
I suspect that the real reason to install an inactive engine allowed to windmill during the flight is that this is a known/analyzed/trained for configuration whereas hanging some cement blocks from the wing (or more realistically extra fuel etc) is not.
Although in theory it would 'might' be possible to 'paper certify' a missing engine configuration that would surely cost a lot more (time and money) than using a real engine as planned.