The problem with that is that the TERPS criteria do not take into account other traffic that may intrude into otherwise cleared airspace. You may well run into another airplane that has inadvertently wandered into 'your' airspace, or that was placed there via controller error or because of an emergency. In a Cat II or Cat III situation, you could easily hit another airplane holding on the runway if you start the go-around at DH or AH.
I think we're talking round in circles here.
Firstly CAT II or CAT III approaches often require immediate go-around actions certainly when operating full automatic under 200R. If there is a runway or protected ILS zone infringement or the preceding aircraft has not cleared the runway or failed to notify the Tower of runway clearance then your approach will be terminated by 'Airline xxx Immediate Go-Around' if you are in the latter stages of the approach. I know, I've had it a few times. That is a direct instruction from ATC and a mandatory follow. Normally the approach separation will allow a normal go-around for a discontinued approach well before such instructions are necessary.
In the event of a possible collision, again, ATC will call for an immediate go-around for infringement of protected airspace. Similar in many respects to the PRM breakout manoeuvres performed in the US. One of the many reasons such approaches are only allowed when LVP's are in force at the destination aerodrome. (ground traffic mapping radar)
For routine go-arounds, and it is a routine manoeuvre, my personal opinion is that it is better to take a long slow deep breath and perform the manouvre without the adrenaline fueled fury I often see in Sim Checks. To be honest the best crews are the ones who discuss the go-around whilst in the approach by just sequencing the events verbally whilst in times of low workload so their colleagues know exactly whats coming. If the instruction is received the PF calls, 'right, as we discussed, I'm starting the manoeuvre now....' press the TOGA switches and perform the Go-Around. Nice, comfortable measured pace.
Shared SA is particularly important for manually flown manouvres which then require rebuilding of the automatics, which lateral mode, what height, what heading, autothrottle etc....?
A go-around is NOT an emergency procedure. The necessity for immediate action depends very highly upon the phase of flight, ambient conditions and the current workload. Yes it will have been briefed prior to descent but, IMHO, after a convoluted RNAV approach into somewhere like Hong Kong or, heaven for-fend, Rio, it is always, always, always worth re-iterating the intended procedure as it might have been forgotten in the workload.
All IMHO of course.