In the assets file, the assets are stored in SRGB but in the software renderer, we first convert them back to linear space, and then back to SRGB, so why we don't store the textures in linear space? So we don't have to go from SRGB to linear...

I think you could do that.

One reason not to is that if you don't perform any operation on the image you can just copy the sRGB value to the frame buffer directly (I think).

Another possible reason not to is that sRGB to linear is a "free" operation by the texture sampler when using a hardware renderer so we might as well keep the source "intact".