I agree completely! And the fact that this wasn't done is the flaw IMO. Which is why our table house-ruled skills and saves into ALL monsters.
As for the feat, that rule only applies if you
have the feat. Nothing to say you couldn't give all Ogres (who I think we could easily see wrestling and shoving each other around since birth) the Grappler feat.
As for the particular move, the shove uses the same mechanics as the grapple. If you have two Ogres, one could shove and the other could grapple if the shove is successful, but since they only get one attack, a single Ogre can't do both as it would take two rounds. It is possible to grapple and then shove prone, but again, two rounds and the target has to not escape the grapple, which is roughly 50/50 again...
Good house-rules are basically the only way to solve it if the table wants creatures to be good at things they
should be good at. Because they were often designed poorly, too many monsters are just bags of HP otherwise. Pity.