Why we need Laplacian for edge detection?
"Need" or "Want"?

Q1:  The second derivative avoids the problem of a gradually changing color being "greyish".

Q2:  Yes.

Here is one:

After advice about detecting focus quality of objects in a photo detected using YoloV3

It is based on how planar the color.  Very planar means no edge.

There are many, many other variations of these techniques possible.