I'll drop the analogies since they're clearly confusing you.

You also seem to have lost the plot here. We're talking about the proper way to address a table of murderhobos and bring them back in line.

Sure, throwing an unwinnable encounter at your players to punish them for their behavior is potentially a way to do that - but in my experience it's more likely to foster an adversarial relationship between the players and the DM. Even if the players get the message it's possible that they might interpret it as "play my way or else".

If your players are all murderhoboing, there's clearly a disconnect in your expectations for the table. The best way to address these kinds of disconnects is through open communication. If you pause things to make it clear that people aren't playing in the way you'd prefer, you can have a genuine discussion about how to roleplay that can take as long as it needs to. You can come to compromises or draw attention to things much easier than if you just throw an unwinnable scenario at them to humble them. If your players are all murderhoboing and all want to murderhobo, maybe you're the odd one out and you need to change your expectations. Or find a new table. But you won't know for sure until you have that discussion on a level that a super-NPC can't get you.

I guess I should stop using analogies then.

The point isn't whether the players are competing with the DM. The point is that there's two people playing a game and one person can just screw over the other whenever they feel like it. Painting that in a competitive setting hits closer to home for a lot of people since they're more likely to have experienced that themselves. It wasn't meant to be indicative of how I perceive a good player/DM relationship.

I'm sorry, I had no idea it would confuse so many people so badly.