The other thing to consider is that when viewing in person, the proportion of our field of view that the sun takes up is way larger than the field of view it takes up when we look at an image of it, unless the image is being projected in a sort of virtual reality type environment. In other words, photos are small objects (even large prints are small compared to our entire field of view), and so a small sun in a small photo just looks extra small, even though it is proportional to the other objects in the photo.
I have yet to see an unmagnified, natural image
Bearing in mind what I said above, I suggest your search for a 'natural' and unmagnified image is an inaccurate pursuit. There's no such thing as a natural image. And there's really no such thing as magnification in photography. It's all about field of view, resolution, etc. An image drawn from a long focal length scope will show the sun taking up a large portion of the frame, but when we view it on a screen, it doesn't mean it is somehow less realistic or 'larger' than reality. I think discussing the level of available detail may be a better indicator of what is 'most natural.' Certainly long exposure photography that has been processed brings out detail we could not make out with the naked eye.
Also keep in mind different people can discern different levels of detail. Part of this is a physical difference in the eye, but its also a brain difference. Visual observers often note how viewing an object for a long time allows you to see more detail. This isn't the same as a long exposure photograph in terms of making something a lot brighter, but our brains are able collect data over time and process the image we perceive over a non-zero period of time. Similarly, many experienced observers note being able to see detail immediately that novices cannot because the novices don't yet know 'how' to see.