Also, in order to make your point about the non-aggression principle, you utilize an example with a lose/lose choice forcing anyone engaging with the exercise to accept a potentially false choice between one death or many. But how often is the choice so stark?

Many people have to make choices which you might consider "lose/lose" situations on a daily basis. Many people make critical decisions on a daily basis. If you're in a position in life where you don't have to make these sorts of decisions often then you're in a privileged position.

An example which is more relatable is stealing. The bible says "thou shall not steal" which would be an example of deontological ethics. A pregnant mother or a father who has a child, or a child who has a sick mother or father, can easily face a situation where they either choose to violate the rule and steal or have reduced options for the person or people they care about. It could be that by stealing they save the life of their child, parent, or friend, but then it violates God's law.

The cost of letting ourselves be forced into this false choice scenario is that we accept violence is acceptable under certain circumstance and then those who want to use violence simply create the circumstance under which we feel it is acceptable.

In an ideal world everyone would cooperate. In a world where there is perfect communication combined with universal enhanced compassion maybe we could have more cooperation. The problem is player A cannot effectively communicate with player B and as a result there is no way for player A to coordinate with player B on a gentleman's agreement for what to do under interrogation. It is shown that when the communication ability exists and both players have a desire to cooperate then of course cooperation is going to have a better overall outcome over many games but over a single game the defector could win.

Some situations are no win situations. Some situations only allow the participant to choose which way to lose from an array of options. So choosing who dies, choosing who suffers, but you might not be able to stop someone from dying or suffering.

References

1. https://en.wikipedia.org/wiki/No-win_situation