sRGB Color profile not showing on display settings

However, I prefer to use sRGB for more neutral and accurate color.

You will absolutely get just the opposite of that.

sRGB is a small color space. It looks dull and kind of lifeless because it's supposed to. It's intended to be a lowest common denominator color space.

If you use sRGB as a monitor profile on all but the cheapest monitors available, then all you're doing is incorrectly stretching out sRGB to your monitor's actual gamut capability.

Such as this. The grayed out area is my EIZO's gamut and color range. The color tinted space is sRGB. If I were to use sRGB as my monitor profile, I would only succeed in creating the most inaccurate color representation possible.

Your monitor only knows the RGB values sent to it. So using maximum RGB red as one example below, 255,0,0 of sRGB would be seen as my monitor's 255,0,0 red instead of where it's supposed to be.

Everything you see as gray would be incorrectly filled with sRGB values, however they manage to fit.

None of the common, canned profiles are monitor profiles. You should never, ever use sRGB, Adobe RGB, or any of the others below the line for the monitor.

The only two shown you should even consider are the ones at the top.