Keyboard Shortcut for placing a clip at playhead

"ctrl + alt + v" does exactly this if you move things from comp to comp.

It's sort of available now but not as a Shortcut - it's in Prefs > General >  Create Layers at Comp Start Time

Also, if you were to drag from the Project Panel to the Timeline and you move into the timeline's layer stems area, you can select which layer index in the timeline you want the new layer to be placed AND if you at the timeline ruler, you can see another timeline indicator that tells you exactly where in time the in point of your layer will be when you release the mouse/drag process.

HTH

That is not what I'm asking for. Maybe I didn't explain properly. The bracket key will move an existing clip on a layer to the play head, but I would love to see a shortcut that takes an asset in the project pane and place it on a new layer at the location of the playhead. Command (control in windows) / will place it at the very beginning of the timeline, but I can find no modifier key that will put that clip at the playhead - unless I'm missing something. Most video editing apps have this shortcut, why not AE?

It already exists. Select the layer and tap "[" to place start of clip at playhead...