I never said anything about a "screaming rush". Your "2-4 seconds" is easily eaten up by the normal cockpit procedure:
ATC: Airline 500 go around; traffic.
PM: Airline 500, roger, go around.
PF: OK, go around, flaps 20. [Press TOGA]
PM: Go around, flpas 20 [Move flap lever]
It can - and SHOULD - be done in an expeditious, but unrushed, manner.
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.
Nope. Once you are told by ATC to go around, and you are on an IFR approach, your clearance changes to "abandon [your] approach to landing", and any previous clearance is cancelled. Unless otherwise cleared, you follow the missed approach procedure. FAA Pilot-Controller Glossary:
GO AROUND− Instructions for a pilot to abandon his/her approach to landing. Additional instructions may follow. Unless otherwise advised by ATC, a VFR aircraft or an aircraft conducting visual approach should overfly the runway while climbing to traffic pattern altitude and enter the traffic pattern via the crosswind leg. A pilot on an IFR flight plan making an instrument approach should execute the published missed approach procedure or proceed as instructed by ATC; e.g., “Go around” (additional instructions if required).