the correct course of action is to fly the missed approach procedure for the instrument approach for that runway.
You and others have missed the point that on a visual approach there IS no "instrument approach for that runway". How would you cope at an airfield with several IAPs, each with different g/a procedures and none of which you have flown?
The only time your proposal is valid is when an aircraft flies an IAP, declares 'visual' and without delay announces 'going around' when I'm sure all controllers would expect what you say. Assuming that the intention of flying a 'visual approach' is to land at that airport rather than push off into possible IMC and the bundu, the visual circuit is where you would go. Initially straight ahead, talk to ATC with intentions, and they will let you know if that is possible or not, in which latter case they would probably 'direct' you.