Cosmo,
We do it that way because that's the way that Airbus designed the aircraft to be flown. As Phantom Driver said, love it or hate it, modern aircraft aren't designed to be flown the old fashioned 'Atlantic Baron' way.
If a G/A is done by hand in a Boeing, then you do it by hand as that's the way that Boeing designed it to be done. As a result, the way that you were trained to fly your Boeing (I assume) would teach you the method and mindset of doing a G/A manually.
As the Airbus is capable of doing the G/A automatically (once we have put the thrust levers in the TOGA gate) we are trained to do it this way, especially when the weather is marginal.
It's not an Airbus vs Boeing thing, it's just the way the two different types have been designed.
Going back to my original point, we talk about the 'Swiss Cheese' Model in CRM..... this incident could have been stopped as far back as ToD when during the brief the PF had said something along the lines of... "As the weather isn't great, I'm going to leave the autopilot in till we get visual. If we don't get visual, I'll hit TOGA, get the Gear and flap up and the aircraft will fly the missed approach which is in the FMGC"