The sun is an incandescent source, yes, but it's far from yellow. Just hold up even the whitest incandescent side by side next to the sun and you'll see what I mean. 5500K versus 3500K. At best the incandescent will look yellowish-orange.
I think part of the problem here might be simply that the beam pattern is different for LEDs versus incandescents. Incandescents usually have a very bright center area surrounded by a corona of gradually decreasing brightness. LEDs are also brighter in the center, but their hotspot is usually way less intense than an incandescent of similar lumen rating. That means less penetration in things like puddles. Also, incandescent beams usually have more artifacts as well as a slight hole right in the middle of the brightest part of the beam. These artifacts sometimes help to pick up more details as opposed to the smoother beam of an LED, or maybe most people are just used to them and anything else doesn't look quite right.
As to color temperature differences, to me anyway LED just seems more natural, at least in an urban environment with lots of neutral colors, or even with foliage which it renders as true green instead of the yellow green it would appear under incandescent. Whites? Again, no contest. They look white under LED, yellow under incandescent. Reds are the main weak point of LEDs but I imagine that deficiency will be overcome while still allowing a sunlike color temperature.
If you want to get technical, then the spectrum of most white LEDs peaks in the blue area, and again in the yellow area. It is weak in deep red and deep violet, and sometimes a little weak in the yellow-green area. Incandescents are rich in reds but progressively more deficient in greens, blues, and violets. The sun is more or less balanced across the entire visual spectrum, with a peak at 555 nm. Certain types of metal halide and fluorescent lamps can come close to this ideal, but none so far have been able to match it exactly.