All games teach moral lessons, whether we are aware of them or not.
Our experience differs slightly – I have seen and played in games where unexpected moral dilemmas were ‘developed’ in a game. The games were engrossing (they only work properly if they are) and some spotted the deeper questions, some didn’t and there were differing reactions at the reveal stage, but some people definitely wanted more.
I am more likely to enjoy participating in a game that has this dimension than one that simply, for example, pits ‘elite troops’ against militias or levies in a killing spree with no moral backdrop.
On the other hand I enjoy games that recreate battles or situations that undoubtedly ended in a bigger ‘butcher’s bill’. A moral conundrum if ever there was one!