Normally you would never convert the color model yourself to prevent losing colors too early (CMYK has a smaller range of colors and once you converted your file there is no way to get these colors back, even when converting back to RGB space). Soft Proofing itself does only convert the image on the screen, not the actual file. It’s to check if the colors would be too off when printed (or looked at on another device with different color model)
This thread also has a lot of useful information on soft proofing and how it works
When soft proofing doesn’t change much on your display, this probably means that your original image is already really close to the color profile you proof against. If you want to make really sure, also turn on “out of gammut” warnings, this will show you wen a color is not available in the color profile that you proof against.
Also, to really make good use of color management, you need a color calibrated display.