This has been my experience as well. I am attracted to bringing games into the learning environment because they can offer unique opportunities for action/reaction/reflection (in addition to other benefits) - but I am indeed more interested in complicated decision making rather than simply choosing Red Team v. Blue Team.
For instance, I would love to see a game like "Papers Please" with a stronger element of consequences. Rather than simply being told you allowed a terrorist through the gates (with a brief cut-away) the consequences of this action (deaths, social destabilization, etc.) would impact the future game play. Perhaps, you decide to actively aid and abet these terrorists (by communicating to them that you will allow them and their compatriots to pass through) - but then you put yourself and your loved ones at risk, as well as increase social instability.
This is already a wonderful game, but I would like to see the premise taken even farther. Games could be a wonderful place to consider and critique decision making and moral choices that are analogous to those we face in real life (even if filtered through clearly fictitious events/circumstances).