Cylindrical grinding operations are generally a better way to reach high precision and better surface finish than any turning operation would hope to. It's the reason that they make "toolpost grinders" for lathes (for shops that don't have and can't cost justify the high expense of a cylindrical grinder of some sort). They make a mess and require huge amounts of care in shielding the lathe ways etc. to keep the grit off, but they will do for the rest of us....on the rare occasions that we need that sort of precision.
Don't think of some dude standing in front of a bench grinder.....rather, think of the part spinning in precision bearings with a diamond trued wheel counter rotating and taking off a few ten-thousandths of an inch. In effect, then, rather than a single point of contact with the work, you have thousands of tiny points of contact that are constantly rotating past the spinning part, creating an aggregate cut that is very smooth and very precise. Depts of cut may typically be in the tenths range.
For even more precision, some applications call for "centerless" grinders in which the part is turned between two wheels....and idler that effectively rides on the back side of the part, behind the grinding wheel and the grinding wheel itself. This way, the only thing that establishes the part dimension is the part itself. It takes any issues of the precision of spindle bearings (or lack thereof) or heating of the spindle etc. out of the equation.
If you think about a normal turning operation, say you had a precision specified down to "tenths" (ten thousandths of an inch or a "tenth" of a thousandth). If your next to last pass yields a part that is only .0005" over tolerance and your tolerances are (-.0002,+.0000), how are you going to make a turning cut that takes off .0005"? Cutting tools tend not to work very well when not loaded properly. Steel is being sheared in normal turning. You could probably finish by hand with an abraisive strip....but that's not so precise. In the cases where this sort of tolerance is called out, the part might be finished on the lathe to within a few thousandths and then finish ground to size.
If you still tend to think of grinding as an inherently crude operation, remember that eye glass lenses (and lenses far more precise than that) are ground using purpose-built machines. There you are grinding both to the point of optical clarity, as well as to a precise curvature to make your prescription different than another.