running the engines much healthier
That's the big one I think, and healthier for those in the aircraft too. With long-term LOP operation I believe you're reducing the risk of mechanical failure, and by operating an all-points monitor you're providing yourself an opportunity to take action before a problem becomes a loss of power.
The Deakin article "Analysis of an In-Flight Engine Failure" is a great example of this. People have argued with me about the safety benefit of a monitor, sometimes stating examples from their flying of when one didn't help, to which I was too polite to suggest they didn't know how to use it properly.
Ask a new instructor why the engine runs rough as you lean past a certain point. I bet 99 out of 100 wouldn't be able to tell you. I'm grateful that this forum provided me with the inspiration to learn until I could answer questions like that.