But here's another simpler reason. This may be, for some, the ultimate explanation/reason. Here's an acceleration profile. There's no ball, it's just a person's putting stroke.
Timing is important. There's some timing in every stroke, whether you're accelerating or not. There's timing in the baseball lob and the car thing too.
If your timing can vary as much as those segments (maybe that's a tenth of a second or something), with impact occurring somewhere in between those two lines, the question becomes this: do you have more consistent speed between lines A or B?
Clearly your speed is more consistent between B.
Well again they are, but many won't feel like they are. The point is to have a curve that maximizes your margin of error:
Even as somebody who has understood the concept from the very first post of this thread, I agree that these two graphs are, BY FAR, the easiest to understand. Well done.
And I also agree they should have been in the OP.
Sadly, though, I imagine you'll still find people to disagree with the concept.