You don't want to convert to sRGB, you want to convert to the display device color space (which in professional displays is often larger than sRGB).

Most desktop environments and applications assume that the source is sRGB, unless specifically tagged (in image metadata).

So you have two points: source (image, video) and reproduction device (display, printer etc). And you convert colors from the former to the later. sRGB may not even come into play if the source image is AdobeRGB and the display is a wide-gammut pro LCD display!