I would naturally make the mental stats stronger than the physical ones, but I just can't countenance an outright dumping of them completely. It just feels too cheesy and ruins the concept for me, something I will NOT do purely for mechanical advantage. A spread like I have above: STR - 8, DEX - 10, CON - 14, INT - 14, WIS - 12, CHA - 16 is about where my head would be at... not terribly different from what I would stat out for a Sorcerer or any other sort of Summoner.
That's good of you to not dump physicals into the ground. I think that, combined with the point buy system, is where alot of the feeling of Synthesist being overpowered comes from. I don't use point buy in my regular home games, instead I use a rolling method geared towards high results, and offer a preset array they can choose after rolling. So, eidolon stats would be likely to offer less appeal to a player in my games.
Come to think of it, my games often run to the high power end, so maybe that's why I rarely experience the problems people describe for some classes/archetypes.