Although some of this information is contained in the Document Info window, that's a really stupid place to put it. Selection is not the domain of the document. THe Document Info panel should contain the document information. LIke the total number of paths, not the selected paths. If anything, selection properties should be listed under info or properties. Those panels make more sense for transient data like selection.
And if Illustrator or Adobe in general ever updates the UI in general for Illustrator, a slide0out parameter panel with tool-specific settings and details would be perfect for this every time you selected one of the pointer tools.

But as previously pointed out, none of this matters if the information for the current selection is included in the workspace footer.

This is neither functional nor effective. The point of the request is to have a permanen (though potentially optional in settings) display of the number of points/paths/pobjects/symbols/artboards currently selected. This would help with so many functions. Especially layered points or objects. Knowing how many you had selected would save a lot of time. And putting it at the bottom of the workspace window would be ideal.

But most importantly, it needs to be a function of the workspace window (that holds the artboards). Having it as a separate panel like the Info Panel or the Properties Panel would not be as useful. Even a "selections" panel would be better than what we have now, but it would not be as good as integrating this into the workspace window.

Suggest increasing the number of statistical 'groups'

This is an old request, and maybe I'm misunderstanding, but I believe you can find this under Window > Document Info, then click the flyout/hamburger in the upper-right and select 'Object' ...I keep that open all the time. Very useful.

I know right, it seems like a very useful tool to have??

did you figure out how to know the number of objects?