HD upconverted to UHD actually looks a little better if the upconversion includes anti-aliasing which most seem to do.
Say you have a diagonal line... aliasing is the stairstepping you inevitably get when you display the diagonal line on a video display with (square) pixels.
You may not be aware of aliasing in your HD images, but it IS there. When you go to UHD you have the opportunity to fill-in the big stairsteps with single pixels that smooth the diagonal line much more than is possible on an HD display. You also have an opportunity to remove the "sharp" pixel at the corner of a stairstep to make that step less coarse. So when you convert HD to UHD, you don't see more detail, per se, but the detail you do see is more distinct and "smoother" along all edges except perfectly vertical or perfectly horizontal edges. The most improvement would appear on 45 degree diagonals, but round objects are improved also, except at the 9-12-3-6 o'clock positions there that single pixel will look about the same on HD and UHD displays.
The problem with SD is you are upconverting it WAY MORE than you upconvert SD to fit an HD screen. When you do beyond doubling the horizontal or vertical resolution, you get into having to interpolate (i.e. making an educated guess) at how you should allocate pixels to make the SD image better. That doesn't always work very well. In fact, SD edges are so blurry that the upconversion process is more difficult to do well. And even the best SD upconversion I've ever seen can't make SD look better on an HD display than it looked on a good SD display. The leap from 720x480 pixels to 1920x1080 is just too big and starts with too little "information". There's just 345,600 pixels in an SD image (1 green dot, 1 red dot, and 1 blue diot make up 1 pixel). While HD has a little more than 2 million pixels, pretty close to a 6x increase. You'd think the 6X increase from SD to HD wouldn't be much worse than the 4X increase in pixel count from HD to UHD. And to answer that, I'd say that converting HD to 6X more pixels would look WAY better than converting SD to HD with 6X more pixels because the SD pixel count is so small from the outset. When you get below a threshold, the intormation density in the original image is so low, that upconversion doesn't do anything to make the image look better. The only way to make the images look better is to get farther from the screen when the information density is as low as SD. On the other hand, HD images have way more information to begin with so upconverting them is not as problematic. FURTHER... to see all the resolution of UHD images, you have to sit around 4 to 5.5 feet from a 60" display to see it all. if you upconvert HD to UHD, you'd want to sit somewhere close to the same distance as if you were watching an HD display, say 7-8 feet from a 60" display (yes, I know a lot of people don't sit that close, but they aren't seeing all the available detail at farther distances, their choice).