Question about the origin of the Greek hoplite shield

[PMBardunias]

This has a boss and is not concave like the Greek designs.

That is the first problem, if it has a boss it probably does not have a porpax and a double grip- the boss usually, though not always covers the fist. For example, early greek shields had many "bosses". In that specific image the main problem is that the shield longer from porpax to top than it is from porpax to bottom, this would be very hard to handle as it would want to fall forward or back. The second image is better, with the cut outs being more robust in construction. If I had to guess, I'd say this is artistic error and the shield depicted had a single central grip- just like the Hittite shields and the Greek Dipylon. Also note the double grip system is oriented the opposite was as a greek Boeotian.

As to why the cut outs. I think for the same reason that thracian pelta are cresent shaped or the shields on the Warrior vase- this is simply two cresents in opposite directions. Have you noticed that hides take on this shape- even more like the old Hititie shields, when dried. Metal ingots shaped like hides look like this too.