When cropping a picture, think of it as printing out the original picture, then cutting it down with some scissors, that's about what you're doing.
After the crop, some software will let you upscale the picture, and depending on the algorithms, it is not entirely possible to improve the cropped photo (also works with uncropped photos), but you can't take a picture with a 300mm lens and crop it + upscale it and expect it to look like the same picture taken from a 800mm lens originally. You might be able to pass it off as a 400mm though, and at least get rid of the distracting elements
