Although quite important, the snap target CENTER is a bit confusing.
This is because new users may not realize that the center of the object depends on the current Pivot Point.
This dependence on the Target by Pivot Point also limits the user's choices.
For example, the user may want the Target to be Cursor and the Pivot Point to be the Median Point (since the cursor can now be snapped and serve as a sort of base point to transform).
This patch proposes to end this dependency by adding the two targets that can only be obtained with a combination of target CENTER + Pivot Points.
These new targets are CURSOR and Bound Box Median:

The icons for the new targets are just a suggestion. And it seems that when saving the file "blender_icons.svg" by Inkspace on windows there is a problem with indentation.

I posted this idea on rightclickselect but it was not well received, (I think because the original idea was also to remove the CENTER target).