A wider color gamut does not mean more accurate color. If the gamut of the recorded images does not match the gamut of your display device, you'll have less accurate color, and in a way that is impossible to fully correct with standard color correction tools. A proper gamut transformation requires you to linearize the color values and then use a matrix transformation. Turning up the saturation is a poor approximation of the proper gamut transformation.
Even if you were targeting a wide-gamut type of display, you'd hardly notice the difference that capture in a wide gamut color space could offer. Natural images don't contain a lot of the super-saturated colors that are outside of the Rec.709 gamut, and even when they do, gamut clamping is rarely noticeable. And recording to a wider with only 8 bits can significantly increase color quantization errors, due to the lack of precision in the Cb and Cr channels.
Computer monitors, mobile devices, and HDTVs all use the Rec.709/sRGB gamut. You'll get more accurate color with less need to adjust in post if you shoot with a color mode as close to the Rec.709 gamut as you can get. Still and Pro are very close to the Rec.709 gamut. (closer than the ITU709 setting, oddly enough)
S-Gamut3.Cine is not close at all to the Rec.709/sRGB gamut. See page 2 of this document:
https://pro.sony.com/bbsccms/assets...ry_for_S-Gamut3Cine_S-Gamut3_S-Log3_V1_01.pdf