They can't feel bigger than the planets. Most planets are already too big for your mind to comprehend, too big to fit into your everyday experience of reality. As such you'll never be able to really feel the difference in size between, say, Earth and the Sun: they're both incommensurably big.
You can certainly fit the concept of a few kilometers in your mind: that's about as far as the horizon goes, at which distance you can still just about make out familiar objects and terrain features. It's a big distance, but you can comprehend it thanks to your everyday experience of it. From there, your working memory allows you to duplicate and juxtapose that distance a few times end-to-end and get a good feeling for what a few dozen kilometers mean as well. But beyond that? You can probably barely get an intuitive understanding of what a hundred kilometers is, you have to start using trick with your working memory. You have to start thinking in steps, you have to group those few items your short term memory can work with into bigger, less accurate sets. And at that point, you are no longer feeling things, you are thinking them.
Just think of what a thousand kilometers is. You can certainly do some maths to figure out how it relates to everyday life figures but that wont help much: your daily commute may be 20 kilometers, and a thousand kilometers is 50 times that. You can probably get a good feel of how much more of a bore your daily commute would be if it were 5 times longer, but beyond that?
I'm sure we've also all watched those videos on the scale of the universe and how various stars compare in size. The first few seconds usually involve Earth sitting right next to the sun: can you actually get an accurate idea of how big the sun is? Or is it just 'big'?
And here's how it relates to the game: the slowest speed in supercruise is 30km/s. I've established we can probably have a relatively accurate grasp of what 30km is, and we obviously have a pretty good intuitive feel for what a second is. From there, 30km/s is a concept you can wrap your head around, but only just barely. The earth's diameter is ~13,000km, if you were to fly by the planet at that speed at about 1000 or 2000km altitude (I don't have the game open right now but I'd think that is approximately the height of the exclusion zone for an earth-sized planet), it would take entire minutes to notice signifcant position changes. Do you think you can get a good feeling for your actual speed and the scale of the planet then? Anybody who's been in a plane flying above a few kilometers and had the feeling the plane was crawling through the air when it was instead going between 300 and 900km/h (speeds which are several orders of magnitude more relatable for anybody who has ever driven on the highway than 30km/s) knows the answer. The further away you are, the faster you need to go to notice any parallax effect.
Now you could think, maybe Frontier should let us move much closer to the surface of stars, to be able to appreciate their scale better, and that's true and would be great, and I'd love being able to fly (painfully slow) through those mass ejection columns. But you would still only get the idea that they are "big", I don't think you would get the feeling of how big (most) stars are compared to planets: 30km/s is just not a feasible speed for flying down to the surface of a star, it's not even feasible for flying down to the surface of a gas giant, and going any faster simply ruins any sense of scale.
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