I know that mice have been used very successfully to study many diseases and conditions that can also affect people. But are mice a good human analogue when it comes to diet?
I don't have time to find citations at the moment, but I seem to recall that the original studies linking consumption of saturated fat with...bad things (high cholesterol, etc.) were originally done with mice and more recent studies involving actual humans have failed to find a connection between consumption of saturated fat and the aforementioned bad things.
I know this doesn't answer your question as much as it introduces more questions, but I recall there being a propensity to use mice for these studies because gene expression based on lineage is more reliable in mice, the effects of metabolic modification are easier to study in mice, and a lot of existing studies are done on mice so it is easier to advance research. I may have read this in a biologists AMA on Reddit, so take it with a grain of salt. I also very much agree that study reproducibility is a major problem. Everyone wants to do the original research, and few want to validate existing work.
It is about compromise. The ideal would be to use real humans for all studies. There are many reasons we cannot do this, about half of them are obvious. (try to come up with the non-obvious ones as an exercise)
Mice are cheap, have a short lifespan, and have less ethical concerns so we use them. They are an okay model of humans, which is good enough to say if something fails on mice don't try it on humans. It is an open question of what treatments would work on humans that fail in mice - but this is impossible to study so we will never know how often this happens. (the fringe "coconut oil" groups put it at 5% from what I can tell)
You've defined above why we use model organisms, but the original question wasn't questioning model organisms in general. I think we should work towards the original posters challenge to validate our models are efficacious, not just normal and cheap. After spending a semester seminar reading rodent dietary studies, I am equally sceptical that mice are a good general model for diet.
The cautious conclusion regarding your question seems to be "mouse models are decent, but we understand the dietary habits of mice much better than that of humans. And sadly, leptin model doesn't translate neatly to humans for reasons not yet fully known but probably partially social in nature"
I don't have time to find citations at the moment, but I seem to recall that the original studies linking consumption of saturated fat with...bad things (high cholesterol, etc.) were originally done with mice and more recent studies involving actual humans have failed to find a connection between consumption of saturated fat and the aforementioned bad things.