As we may change the FMC selected rwy fast enaugh, we will have also the go-around route selected on FMC. After selecting 'go-around' next step will be to follow the selected route,which is for the new rwy.
I've been asking many of my coleagues what will they do in case of go-around...most common answer was 'I'll ask for vectors". Next answer was 'follow the go-around for new assigned rwy'...
One of the reasons was , as said before, at many airports with parallel rwys, the go-arounds are divergent, so as to avoid collision risk.
And if you expect us to follow the initial rwy go-around procedure,and we follow the new assigned rwy procedure, you think you will always be able to make yourself heard and understood fast enaugh over the radio?
I've personally seen a scary situation with two ,same company, aircrafts when one did a late take-off and the other one did a go-around above the previous one. The controller had no chance to make itself understood by the pilots, as both crews were fully occupied, and had also, almost the same callsigns. We just stood and watched...hopefully god was also watching that day.
So,try to make it simple..and safer.No side step...or issue the go-around instructions with the side-step clearance.