Why? If you are sent around from, say 1500ft, on an approach due to a blocked runway or an incident on the airfield you are cleared down to DA/MDA on the approach anyway. There is absolutely no reason to immediately hit the TOGA buttons and begin the procedure. ATC don't care when you do it unless they pre phrase with immediately.
A quick run through of what you are about to do makes the procedure far more simple.
If I'm unstable at 1000' and my co-pilot calls go-around then I'll go around but I won't rush it.
If I'm at MDA/DA and the call is made THEN I'll punch the TOGA switches immediately or in the case of a baulked landing or a go-around in the latter stages of a CAT III landing. Otherwise take your time.
Obviously PRM procedures not withstanding.
More people screw up routine go-arounds and overspeed the flaps or forget the gear by rushing so why do it?