Why is TO/GA button disabled in 777 with weight on wheels or below 2 ft RA?
Boeing's officially stated reason in the report is:


  ... to prevent pilots from inadvertently activating TO/GA mode at or after touchdown. Inadvertent activation of TO/GA could result, among other things, in the aircraft departing[1] the runway. ...


[1] As in runway overrun/excursion.

Which is in accordance with AC120-29A (also from the report), where:


  ... If an automatic go-around mode can be engaged at or after touchdown, it should be shown to be safe. The ability to initiate an automatic or flight director go-around at or after touchdown is not required or appropriate. ...


It's either Boeing did not want to, or could not, demonstrate it would be safe, hence the inhibition (nor is it a required system). Boeing does not elaborate on the "among other things".



Some remarks on the 777's TO/GA switch:

Applying full power on a go-around on a 777 after consuming most of the trip fuel is tricky because of how powerful the engines are. It would produce a big nose up.

For this reason, pressing TO/GA – unlike most planes – does not command full power, rather enough power for a 2,000 ft/min climb. Pressing TO/GA again, would command the full power (source: FCOM 6.4 Page 51).

So there's logic involved.

The closest Boeing patent I found was the Total energy based flight control system published in 1984, which does exactly that, among other things. A system for commanding elevator and/or thrust based on the plane's current and commanded energies for a target flight path. (Download the PDF for the logic diagram.)

For that to work, the plane needs to know its current flight path. If the wheels touch, and with the drag of the ground friction, which is unaccounted for in the logic, the system can't function as designed, or additional logic will need to be added and certified.

Note: The same inhibition, climb target logic, and a double-push for THR REF is also on the 747-400 (source: FCOM 4.10.17). The patent's date makes it plausible that the 747-400 was of the first to receive this system, and it was carried over to the 777.