Palm TOGA buttons work quite well, mainly because the thrust levers have to be open before you can access them.
Perhaps these Boeing TOGA buttons should only be pressed after the thrust levers have been opened and the FCOM which reads 'A missed approach is accomplished by selection of either TOGA switch' should include some mention of advancing the thrust levers and the FTCM should perhaps read 'advance thrust levers, push either TOGA switch... ' instead of simply the 'Push either TOGA switch, call for flaps 20, ensure go-around thrust for the nominal climb rate is set and monitor autopilot performance'.
The almost total reliance on automation is quite clear.
If this incident had been a go-around at low level with a TOGA button failure (ie. Not a balked landing after a touchdown), the results would probably have been very similar.