I think you're right about internet/social media perpetuating the sense of necessity for an alpine start. Although I will say that the argument about not needing to hike after the sun goes down actually can be valid. Length of day is about 13 hours this time of year, which I think is just a bit faster than most people take to hike the main trail.
Hypothetical example, not taking into account weather: if I was planning to spend 15 hours on the trail, personally I'd rather have the 2 dark hours in the morning on fresh legs rather than at the end of the day when I'm just trying to drag my sorry self back to the car. Note that most tumbles on trails in general usually occur on the descent.
This can be a personal preference thing as well. I myself find that I am a whole lot more excited about the hike when I start than when I am coming down: the descent is a little anticlimactic. For this reason, I prefer being able to enjoy the scenery going up rather than coming down (at which point I am less in tune with things).
As for falling, this can be an issue. But compared to many other hikes, the Whitney trail is a whole lot sketchy in terms of grade and slipperiness. Falling is less likely on Whitney than, say, South Sister. Also headlamps are pretty good today (especially 18650 headlamps). When you can literally strap the lighting power of an automotive headlamp to your forehead, having daylight is less critical.
