I guess I look at this differently.
C selects the clip under the pointer. That’s how it works. ‘C’ does not select the clip under the playhead, so if you do not want to select the clip under the pointer, don’t hit ‘c’.
If you look at the playhead, the clip that is underneath it is selected by default when you pause playback. When you stop playback, the top most clip that is under the playhead is loaded in to the inspector. That’s what this little ball means:

So to select the clip under the playhead, don’t hit ‘c’ as that will select a clip under the pointer. Hit select above/below or next/previous, and you will be able to select the clip under the playhead. And toggling the skimmer (and clip skimming) on and off will focus the select functions to the playhead.
I guess if you were to ask for something, it would be to add a command that is to “select clip under playhead” which, essentially, is ignoring the pointer.